As I crossed the hot, crowded concourse of Gare Montparnasse, Paris, I walked past a jazz band blasting out Sweet Dreams (Are Made of This). Approaching the ticket barrier, I was alarmed to see that the musicians had fallen into step behind me while still playing. They were not serenading me, however, but my train. This was the day the high-speed service from Paris to Bordeaux became even faster: just over two hours rather than three and a quarter. If you’re travelling from London, the small adventure of the change in Paris is involved, transferring from a Eurostar to a TGV train, so it takes five hours and 50 minutes.

The trains to Bordeaux are either the new Duplex – or double-decker – ones or older, single-deck. Both would shame any British train.

On the new design, if you travel first-class, you can enjoy seats that swivel to face the direction in which you are travelling. While I settled into mine, the brass band threw their straw boaters in the air as our train departed.

Exactly 100 minutes later the first sprawling vineyards of Bordeaux came into view – giving me the feeling that I was about to fall into a vat of wine. Not so unlikely in this area: Bordeaux takes its wine drinking extremely seriously – last year it opened a mega museum La Cité du Vin. Located in a glass building that looks like a disorted bubble, it offers expert-led tasting sessions and interactive displays. The unusual shape of the building is meant to represent the swirl of wine vapour in the glass, although I couldn’t help thinking of a giant Ugg boot. Either way it’s the ultimate expression of Bordeaux’s stylish and high-tech epicureanism.

Futuristic design and ancient heritage (wine has been produced in the region since the 8th century) work well together here. Even the trams have a space-age look that contrasts effectively with the formal, 18th-century elegance of the town centre, full of buildings in golden limestone.

Twenty years ago, they were black from pollution. The occasional dark one survives like a bad tooth – a reminder of the bad old days when Bordeaux was a stuffy backwater whose population fled to the resort of Arcachon on the Gironde estuary every weekend.

That was before the city was transformed by its long-term, cycling mayor, Alain Juppé, who introduced trams, hire bikes, pedestrianisation schemes, and a wave of young entrepreneurs. Four years ago a survey ranked Bordeaux as France’s second-favourite city after Paris.

Sitting on the terrace of the pretty, slightly battered-looking Bistrot des Quinconces at 7pm on a lovely summer’s evening, a glass of wine was not so much called for as demanded – especially as I’d managed to avoid the bar on the train. With my suitcase tucked under the table, I passed a satisfying hour with half a bottle of Graves dry white and a fried duck’s breast with frites.

After coffee, I walked to my hotel, Le Boutique, cleverly inserted six years ago into an 18th-century town house. Then I explored the old town. Medieval lanes thread drunkenly through the grid of streets. Sometimes a turreted gatehouse – a remnant of the original city wall – appears like a film set for a fairy story. The focal point, and the culmination of the Cours de l’Intendance (the smartest shopping street) is the Grand Théâtre. Built in 1780 on the site of a Roman temple, it looks exactly like one.

Just off the square is the Bar à Vin, on the ground floor of the Bordeaux Wine Council HQ. It has classical mouldings, Scandi-modern furniture, and a stained glass window featuring a well-toned Bacchus. As the sun streamed through the red and gold glass, I enjoyed a glass of Château Cantelaudette, Graves de Vayres – excellent, and only €2.50.

Later, I walked north to where the 18th gives way to the 19th century and the pretty rue Notre Dame, where chic and arty boutiques lurk behind curtains of ivy.

I retreated from the glare of the sun into the Museum of Contemporary Art, located in a vast, reclaimed warehouse and maintained in a dark and crypt- like state. Most of the installations conveyed a chamber-of-horrors frisson (corpse-like mannequins a speciality), as though taking their cue from the building’s gloom.

Back in the pretty courtyard of my hotel, I ate tapas: avocado, salmon and a fried egg on a buckwheat blini followed by cod in a garlicky pil-pil sauce – delicious comfort food. As with everything else in this city, past and present are harmoniously allied here and it couldn’t be a more enjoyable combination.

Way to go

Eurostar tickets to Bordeaux start from £55. Doubles at Le Boutique Hotel Bordeaux from €200 (hotelbordeauxcentre.com)

Andrew Martin’s latest novel is Soot (Corsair, £14.99). Order a copy for £12.74 at bookshop.theguardian.com