The train submerged me beneath polite Villiers to the sound of the Rhine emerging from chaos at the start of Das Rheingold, and then the Rhine Maidens enticed me as fashionable Paris went to work. A Francophile once pointed out to me that most French clothes look as if they'd been bought at C&A ten years ago, and yet the wearers always seem to look so immensely stylish. It must be to do with being French, I suppose. I look French, I've got a swarthy skin, dark hair and a serious expression most of the time. I usually get spoken to in French when I'm in the country, and I'm never bothered by touts or scammers. And yet I always feel scruffy when I'm among French people.

I was bound for St-Eustache, a church I remember loving when I'd last been inside. Back then, there was a tremendous view of it across the gardens of Les Halles, but that is currently impossible while the reconstruction of Les Halles takes place. This was the site of Paris's vast fruit and vegetable market, the equivalent of London's Covent Garden. It was demolished in the 1960s, and straight away everyone knew it was a mistake. Even the signs outside the shopping centre that replaced it admit that the destruction of Les Halles was 'a bruise on the face of historic Paris'. If any good came of it it was that from then on Parisians fought tooth and nail to preserve the historic centre. The Quai D'Orsay railway station was next scheduled for demolition, but it was saved, and today is a fabulous art museum. Now, the ugly underground 1960s shopping centre is being reconstructed, but it won't bring back Les Halles, of course.

St-Eustache was as good as I remembered, another cathedral-scale church of the 16th and 17th centuries, a time at which we had stopped building churches in this country, and would not build the on this scale again for another 200 years. it's flamboyance shows us what English Gothic might have become.

 I wandered westwards to the Pompidou Centre. What a dramatic sight this building still is, and I enjoy people calling it the first post-modern building in Europe, because it means that I can correct them. The young Norman Foster beat Richard Rogers by five months, and his curving black glass Willis Faber building can be found not in Paris or London, nor in Berlin, Amsterdam or Barcelona, but in homely Ipswich in Suffolk. I cycle past it most days.

But this is not to cast a shadow on the Pompidou Centre, which has one great advantage over Willis Faber in that it is a public building. As at Musée de Cluny and the arc de Triomphe earlier in the week, I did not have to queue, I just walked straight in. Were they expecting more tourists in Paris this year, and they didn't come?

Up the long ranks of escalators to the top then, the 96 degrees sun burning through the plastic coving, the regular openings filling me with dizzying fear as I looked down in the square below. There were about half a dozen hippies down there making and selling jewellery, seemingly oblivious to the intense heat. They were as brown as berries. I am sure they were there when I last visited in 2000.

The main exhibition was the first major retrospective of Roy Lichtenstein, an artist I have always greatly admired. About 250 works follow him through from the late 1950s  to his early death in 1997. Everything is striking, everything makes sense. In his middle years he moved away from pop art to something like abstraction, but you are always conscious that it is not abstraction, rather a facsimile of what abstraction might feel like. Even in his final works, which explore Chinese river themes, he shows that he has no interest in the subject so much as in the way it might be reproduced. A life's work which created a genre.

I wandered pleasantly through the two floors of modern (1900-60) and contemporary (1960-2013) and was amazed to discover that four hours had passed. I could quite happily have spent another four hours in the Pompidou Centre. I think it is one of the best galleries in the world.

Slightly sated by modern and contemporary art, I went into St-Merri, the large medieval church which sits to the south of the Pompidou Centre. This is a fine building, late medieval becoming early modern. There is a vast quantity of late 16th century glass, but some of it is hard to photograph because the easterly side chapels are full of ecclesiastical junk, piled up to keep it out the way. The church is very much in the liberal tradition of Taize, World Youth Day and liberation theology, which I liked very much, and I expect that they are very pleased with the new pope. The church is the chaplaincy for Les Halles and the central streets of the city, and was obviously very energetic in its youth work. It was a shame they were so embarrassed by their old stuff, they didn't need to be. In the south aisle there was an excellent photographic exhibition of portraits of villagers in Guinea-Bissau holding up products they'd either grown, farmed or hunted. The villagers are set back in monochrome, the produce in vibrant colour.

Guinea-Bissau villager with produce

I caught the metro to Cardinal Lesmoines and walked up through the Sorbonne to St-Etienne sur Mont. This was the church I found locked on Tuesday, but coming back I knew it would be open, and it was. The interior is a fabulous confection, the barley sugar spiral staircases lifting to a rood loft which might be a bridge in Venice. This level runs as a conceit around the arcades of the church, creating the effect of a triforium with clerestory above it, filled with vast windows of coloured glass. A wonderful church.

Outside, the steps where Owen Wilson waits in Midnight in Paris were now empty, the wine bottle gone. I resisted sitting down on them (someone might see me) and wandered down Rue de Montagne Sainte-Genevieve, the winding road up which comes the car which will sweep him away to the 1920s. Just below the church was a second hand classical and jazz CD shop, where I sheltered from the sun for a while and bought three CDs for 3 euros each. Wagner's Faust songs (Wagner's music forms the basis for several instances of black humour in Woody Allen's work), Thomas Beveridge's Yizkor Requiem, an interleaving of Jewish and catholic liturgies, and Percy Grainger songs, which seemed oddly parochial in such an exotic spot. A couple of doors down was a cafe with the frontage wide open, a small group of friends drinking pastis and chatting, other people sitting alone and reading over a coffee. Perfect. I sat with a double espresso and carafe of water for half an hour or so, finishing Andre Makine's Requiem for the East and watching groups of serious-looking young people photographing each other on Woody Allen's steps.

I walked on down the hill and took another look inside St Julien le Pauvre, before crossing to the Île de la Cité and walking past the west front of Notre Dame, then east and crossing the bridge to the Île de St Louis, which is home to a wealthy tourist district, all posh clothes shops and expensive restaurants. At the heart is the large, handsome church of St Louis, mostly a 19th century reconstruction but utterly tasteful and seemly inside as befits its district.

The local school sits beside the church, a 19th century building still in use for its original purpose. Outside a sign remembers 'the children of this school taken away during the Nazi occupation because they were born Jewish. They were killed in the death camps. Remember them.'

I crossed back to the Rive Droit and climbed up beyond Rue de Rivoli to the Rue des Rosiers, the heart of the Jewish district. Young Jewish men in dark suits and skull caps bustled about outside a synagogue. A group of them stood with a beat box and video screen outside a kosher butcher's, playing hip hop and showing scenes of the Holy Land. I wasn't sure what they were doing. As I walked past, one of them grabbed my arm. 'Monsieur! Vous etes Juif?' No, I wasn't, I told him politely, so I never found out what it was.