A Parisian friend of mine recently remarked that Parisians are rude, and you just have to get used to it, but honestly that has not been my experience at all. I have found Parisians consistently polite - no, that word is not formal enough. They are courteous. And they appreciate and respond to courtesy in others. I have experienced this, and seen this, again and again, in shops, cafes, museums, on the street, at crossings, and so on. They show deference to the elderly, and indulgence towards children. They smile when dealing with strangers. There is a formality to Parisian life that allows people to rub along together.

In the Monoprix today, I was exchanging pleasantries with the woman on the till when she said something I didn't understand, and I instantly revealed my Englishness. She continued talking to me in English, and I suppose that her English was about as good as my French - Villiers is not a tourist area. She finished by saying "I am so glad you came to my cash so I could practice my English."

Certainly, you often hear the sound of drivers pressing their horns in the centre of Paris. But almost always this is when cars have stopped at lights, and how can you sit in the centre of Paris staring at a traffic light, when there is so much else to look around at - beautiful buildings, beautiful women, the bustle of life. No wonder drivers miss when the light turns green, and have to be reminded by a driver behind them.

I decided that today was a day for going underground, and I set off to Montparnasse to visit the catacombs. These are a vast maze of tunnels under Paris originally used for quarrying the stone out of which the city's main buildings are constructed. In the late 18th Century, the state of the city's churchyards had become so disgusting that the city removed the bones from all of them. They were brought here at night, the carts coming from the centre of the city accompanied by torch-bearing acolytes and priests chanting the requiem Mass. A skull count showed that almost six million corpses were removed in this way. They were buried deep underground, but these people being Parisians the skulls and bones were arranged in a neat and methodical way, a meaningful chaos. Layers of tibia and femurs are crowned by a layer of pelvises and skulls, and so on. Each churchyard was grouped together, and a plaque shows which parish provided the skeletons.

The work was interrupted by the French Revolution,which provided plenty more corpses for when the work was resumed. Altogether about a kilometre and a half of tunnels were filled with the remains of dead Parisians, and you can walk through them on a winding route under the streets around Montparnasse station. In fact, this is just a tiny fraction of the tunnels. The catacombs extend for hundreds of kilometres under the city, many of them rarely explored and difficult of access. Because of this, they are regularly broken into by intrepid adventurers, and many legends have grown up about parts of the network. However, my favourite story is one which is true.

In 2004, a group of police cadets on a training exercise were given the task of tracking an imaginary criminal in a part of the network which was little known. They got into the system through a manhole, and when they were about a hundred feet underground something rather odd happened. They triggered a motion sensor which set off the sound of barking dogs. Thinking that it was part of the exercise, they headed onwards only to come out into a vast cavern which had been fully equipped as a cinema. An anteroom had been equipped and fully stocked as a bar, and there was also a film storage room. When the cadets reported what they had seen, the electricity board were sent in to work out where the invaders were getting their electricity from. Instead, they found the wires all cut, the equipment removed, and a sign saying 'Don't try to follow us. You'll never find us.'

Perhaps the cineastes had got fed up with waiting to get into the system officially, because this was the only place all week that I encountered a serious queue. Worse, I was just in front of a small group of people who talked constantly in very loud voices. She was an American who obviously lived in Paris, and they appeared to be young relatives who'd come to stay. She was taking them down the catacombs, and the price to be paid for this by the poor kids was to suffer her pretentious nonsense. She went on about spirituality, and homeopathy, and psychoanalysis, and the inner energy, and so on. Fair play to the kids, they responded enthusiastically enough. 

And then she got out some of her stream of consciousness poetry, and started reading it in a loud voice. Well, goodness me. I was put in mind of something the graphic artist Alan Moore said when he was in Hollywood helping turn his 'V for Vendetta' into a film, and he was asked at a director's lunch why he lived in Northampton, England. "Because it keeps me grounded", he replied, and I thought that this was exactly right. It was like the opposite of this pompous woman, although to be fair to her I expect that if I went to live in Paris I would also disappear up my own backside.

The catacombs are brilliant, worth every minute of the queuing time, worth every insufferable stream of consciousness adjective. And then I went and did some shopping. I pottered around in the tourist shops of the Latin Quarter, gazing in awe at the kitschy t shirt designs, the snow globes, the Eiffel Tower thermometers, the chef's hats and aprons, the gros bisous scarves, the ugly jewellery and the rest. Passing these and instead buying some things for which my family might reasonably thank me, I crossed back over the river to go church exploring.

There were three churches close together near the Louvre which I very much wanted to visit, and so I set about them. The first was St Germain l'Auxerrois, which sits directly opposite the eastern entrance to the Louvre beside a magnificent bell tower, which though attached is not actually part of the church at all but a part of the mairie of the 1er arrondissement next door. St Germain l'Auxerrois has a beautiful frontage, and you step into a thrilling interior. This church is almost all of the late medieval period, the French opting for 'flamboyante' when we went perpendicular. The late 19th century glass which replaced that destroyed in the revolution is delightful, a touch of Aubrey Beardsley meets Charles Rennie Mackintosh.

Outside, I watched half a dozen teenage Roma girls with mock petitions try to get tourists to sign them. Nobody was fooled, and in the end the girls gave up and went and lay down in the sun. The idea is to get people to sign for what seems a worthy cause, and then the small print is pointed out to them that they must contribute 30 euros to the cause if they have signed the petition. There are also suggestions that the girls crowd round and pickpocket the signer, though this lot didn't really look up to that. I'd seen some of their colleagues trying to work the same trick outside the Pompidou Centre earlier in the week, and no one was fooled there either.

There had been a lot of publicity recently about Paris scams, and given the strength of the Euro there was a real danger that people would be put off coming here. Francois Hollande's socialist government had worked hard to remove the Roma encampments from around the city, and I certainly did not see the most famous Paris scam of all, the lost ring trick, once during my week in the city. The bracelet scammers are still at work on the steps of Sacre Coeur as we shall see in a moment, but they, of course, are not Roma.

I wandered westwards to St Roche. This huge church is late baroque, built in two separate campaigns of the mid-17th and early 18th centuries under two different architects. Soon after it was completed, the Marquis de Sade was married here. A large dome sits above the altar rather than at the crossing, and beyond it are two nested chapels, one seen through the easterly screen of the other, a pleasant conceit. I quite liked the painting and the gilding, though the statuary was a bit much for my liking, and I do like a bit more coloured glass. But the most moving feature is the memorial to France's deportees, those sent to the concentration camps and death camps in 1940-44 by the occupying German forces and the Vichy French collaborators. More than 60,000 French people lost their lives, many of them Jewish, others including resistance fighters, catholic priests, socialists, people with learning disabilities, Freemasons, Jehovah's Witnesses and Roma. The memorial features the names of the camps and the number of French victims in each, and behind each name is a jar of soil from that camp.

Lost in thought, I headed on to Notre Dame des Victoires, taking a mazy detour through Paris's increasingly busy Japanese district. I got to the church to find that vespers was about to begin. I stood in the open doorway and took a long shot of the opulent 19th century interior, hundreds of candles flickering, hundreds of people on their knees.

On my way up the steps I had given a euro to an old Roma lady who was begging there - as in Ireland, as in all civilised countries, begging is legal in church doorways in France. She was here with an old toothless man, who looked as if he was probably North African. She was wrapped up in a long headscarf, her face in shadow. As I stood there looking inside, she came up to me. "Monsieur! Vous etes Catholique?" I told her I was. She pointed in at the statue of Mary at the far end. "La bonne dame - Elle  nous protege!" She pointed to my camera, and then touched her heart.  "Photographe-moi Monsieur!"

She stood in front of the church railings, theatrically motioning me to wait, and removed her scarf, shaking out her hair. I saw that she was not an old lady, but thirty years old at the most, her hair raven black. Her face was hardened by poverty, but she still carried the bloom of a young woman in her eyes. She adjusted her scarf, smiled, and I photographed her.

 Roma lady outside of Notre Dame des Victoires

 She was excited by looking at her face on the screen, and asked me to give the photograph to her. I explained in my best French that this was not possible, but she laughed and waved her hand. "Envoyez la photo a l'eglise! La prete, il me donne la photo!"

 I agreed, and wandered on. I don't really know why she wanted me to photograph her. She certainly wasn't a pickpocket, and she didn't ask me for money beyond what I had already given her, which wasn't much. I like to think she wanted to be photographed so that she could look at it and remind herself that she was, in fact, beautiful.

In the evening I wandered back up into Montmartre, hot on the Amélie trail again. Just north of Abbesses metro station is la Rue des Trois Freres, and here is the premises of Monsieur Collignon who owns the fruit and vegetable business. The shop still looks exactly like it does in the film, because the owner has kept the trimmings applied to the shop for the film, including the 'Collignon pere et fils' sign. As well as fruit and vegetables, the outside display includes some garden gnomes and a discreet bin of Amélie posters. Beside the shop is the doorway to the apartment block where Monsieur Collignon lives. Here, Amélie replaces his personal belongings with smaller sizes to punish him for his treatment of his learning disabled assistant. The film used this actual apartment block for those scenes.

Not far off is the small arts cinema where Le Fabuleux Destin d'Amélie Poulain had its premiere before an invited audience of local shopkeepers and residents. This is the cinema where Amélie turns around to watch the reactions of the other viewers at dramatic moments in the films. The wall paintings were the work of Jean Cocteau, and the cinema achieved a certain notoriety in 1930 when there were riots outside in protest at the first showings of Dali and Bunuel's l'Age d'Or.

I climbed up into the heart of tourist Montmartre, which was like Blackpool in high season. I enjoyed it as a spectator, a flâneur, a wanderer. I felt like John Betjeman enjoying watching simple people going about their simple pleasures. The noise, the ice creams, the crepes! I passed le Consulat, the restaurant where Woody Allen dines alone in maudlin fashion in Everyone Says I Love You, and which was reconstructed in precise detail on a Hollywood sound stage for April in Paris. I continued over the hill, past Paris's last vineyard, to au Lapin Agile, a country auberge in its style and setting, but in its time a remarkable cabaret. Both Picasso and Modigliani paid their bar bills here with paintings rather than money.

I wandered back up to the top of la butte. This is by far the most touristy part of Paris, and almost all of the tourists were couples, dewy-eyed and in each others arms, or grumpy husbands and wives  reprimanding their children. For a moment, just for a moment, I felt a bit lost for being on my own, for being single, for being a voyeur. And then the moment passed. I turned the corner to glorious Sacre Coeur, the most romantic and photographable church in all Paris. But as I say, I was on my own, and in fact Sacre Coeur is the only church in Paris where photography is not allowed. There were hundreds of people inside, praying, lighting candles, wandering, shouting, taking photographs, being told off for taking photographs. The vast range of 1950s modernist glass is superb, some of the best in the world. I would have loved to have spent an hour or so documenting it. But it was not possible.

I sat for a while, and then wandered back down the hill. Everywhere, signs reminded you to beware of pickpockets, but there were none of the groups of Roma youth of days gone by. What on earth has the Hollande government done with them?

 At the bottom of the steps, handsome African men were pulling the bracelet scam. This involves approaching someone, usually a young girl, gesturing for her wrist, and then tying a wool bracelet on to it. The bracelet is not easily removed, and once in place a demand for payment is made, usually about 30 euros but falling swiftly. I saw a group of them pull the trick on two young girls who then laughed and ran off up the steps without paying. For a moment, the group of men looked at each other, as if deciding whether to pursue them. But then they just laughed, and looked around for other victims. As I walked down to the Anvers metro stop, a police car stealthily made its way up to the base of the stairs.