Yet all these grands galleries suffer not only from the crush of tourists, but from the constraints of "public" art. Compromise is unavoidable when balancing innovation against populism, with its inevitable bias towards the old and the established.
The Fondation Cartier has no such problems. Built on the wealth of the jewellery empire, it has the cash and verve to ignore such constraints. It is unashamedly modernist, as is the steel and glass showcase of its spanking new headquarters on the Boulevard Raspail.
If you have the time, you can approach the Fondation on foot from the banks of the Seine. An hour or so's stroll could provide a pleasing preface. From the Ecole des Beaux Arts on the Quai Malaquais, continue past one of Paris's oldest buildings, the 12th- century church of St Germain des Prs. Observe the Hemingway and Henry Miller wannabes in the Cafs de Flore and Deux Magots, then stroll on past the private galleries of the rues Buonaparte and du Seine, whose prices, not to say punters, reflect the upmarket slide of the quarter as a whole.
Here, the Fondation Cartier is well placed. It is one of the few major European galleries with the resources to sponsor new talent, commissioning individual items and whole bodies of works from young artists both French and foreign. In the words of its curator, Herv Chands, the Fondation serves "as a tool for artists to invent, create and encounter challenging experiences". It is a recipe for the unfamiliar - even, depending on your taste, the unfathomable.
A few internationally known artists are represented in the Fondation's 600-strong collection, including Ian Hamilton Finlay, Julian Opie, Richard Hamilton and Gilbert & George. But don't expect to see any of their works in the Boulevard Raspail - most of the collection is permanently on tour in galleries across the world. Instead, the Fondation's wide open spaces are given over to transient exhibitions lasting between one and six months. The longer shows are, for the most part, showcases for specially commissioned pieces, sometimes presented with examples of the artist's other work. These range across the gamut of the arts, from painting and sculpture to video, photography and multi-media installations. Into the latter category falls the main current exhibition, Raymond Hains's "The Three Cartiers". This uses a combination of film, photographs and objects to mesh the lives of explorer Jacques Cartier, the founder of the jewellery firm (also a Jacques), and photographer Henri Cartier-Bresson, in a web of intriguing visual puns.
Recent examples of the month-long shows have ranged from the stark, still beauty of Seydou Keita's photographs of his compatriots in Mali, to the "white works" objets trouvs of Herbert Zangs, who once responded to a critic's enquiries by declaring, with wonderful Teutonic angst: "My life, like my art, is too hard to understand."
The only truly permanent feature of the Fondation Cartier is the building. Completed only last year, it was designed by Jean Nouvel, one of France's most celebrated modernist architects. He was the man behind the stunning blend of high-tech and traditional orientalism of the city's Institut du Monde Arabe. The Cartier stands on the site of the former American Cultural Centre, an ironic riposte to the McCulture which is sweeping across so much of Paris.
In the more distant past, this site was home to the romantic writer and statesman, Franois Ren Chateaubriand. A cedar he planted in 1823 now forms the centrepiece of a new garden, devised by the appropriately named Lothar Baumgarten. The curving branches of its trees are reflected in Nouvel's massive squares of glass like sinuous lines mapped out on a graph: on a cloudy day, the reflections seem like silhouettes projected on to a screen of shifting greys.
GETTING TO PARIS: BA (0345 222111) has a World Offer return flight for £68 (book by 2 March, travel out by 31 March, stay at least one Saturday night and no longer than a month). A similar offer in April costs £85 return; usual APEX fare is £115 return (book at least 14 days in advance). Eurostar (0223 617575) return: 1st class, £195; Standard, £155; APEX £95 (book at least 14 days in advance, tickets cannot be exchanged or refunded).
Kirker Holidays (071-231 3333) offers a two-night break including return flights, transfers, accommodation and Seine cruise from £209 per person; a week with a similar package is £374. VFB Holidays (0242 240339) offers a two-night break with return ferry tickets for £126 per person for at least two sharing a car; with flights, £201; by Eurostar £198 - add £31 per person per night for a longer stay.
FINDING THE FONDATION CARTIER: The Fondation is at 261 boulevard Raspail (010-33-1-4218-56-51). Open daily except Monday, noon-8pm (10pm Thursdays). Admission Fr30 (Fr20 for under-25s). The nearest Metro station is Raspail (lines 4 and 6).