There is not a lot of art that can compete with a building by Frank Gehry Hon RA, though Gehry himself rejects the idea that he is a sculptor, instead claiming in interviews that he is an architect trying and failing to achieve painterly effects. And few Gehry buildings – maybe none – can compete with his own masterwork, the sinuous, titanium-clad Guggenheim Bilbao of 1997. The new Louis Vuitton Foundation in Paris, however, can lay a strong claim. For me it is his best building for years, with an indulgent budget of nearly £89m to suit.

Sited controversially in the supposedly untouchable Bois de Boulogne in Paris, next to the children’s zoo, this building shows that, at 85, Gehry still has plenty of creativity in him. It works as a piece in the round on its own terms, and in the context of the forest backdrop of the Bois. It’s a very ambitious, fluent piece of work, described by Gehry as a ‘vessel’ for contemporary art – the art in question being that of the French luxury goods conglomerate LVMH, which includes Louise Vuitton, Moët, Hennessy and Dior.

The group is headed by Bernard Arnault, an art collector himself, as people in his position tend to be. He likes his Rothko and his Warhol. But what may be more pertinent here is that he initially trained as an engineer and ran the family construction company for a while in his youth, working with architects.

In the building you will find, among its 11 gallery spaces, numerous vivid works by Ellsworth Kelly Hon RA and a specially commissioned installation by Olafur Eliasson, Inside the Horizon, a curving colonnade in bright yellow and mirror glass, down at the ‘grotto’ lower level next to the shallow pool in which the whole building sits. The permanent collection display will change constantly – at the start there is a large sculpture, Man in the Mud (2009), by Thomas Schütte in one very high gallery space and, in another, Cerith Wyn Evans’s AFLOAT, a suspended fluted-glass work. The inaugural show in the gallery for temporary exhibitions was devoted not only to Gehry, but specifically to his many working models for that very building. Across town at the Pompidou Centre, there is a Gehry career retrospective.

In a way, the collection is less important than the building, which acts as a deconstructed glasshouse and belvedere, rising above the forest canopy. A viewing terrace at the top, in the open air but sheltered by the curving shimmering glass-clad ‘sails’ of Gehry’s composition, provides carefully framed views of the forest and of Paris – notably the Eiffel Tower and the nearby La Défense business district. Overall, it is a place of multi-level public promenade, and a ticket includes entrance to the zoo alongside – also owned by the company, naturally.

If Bilbao (though relatively late in Gehry’s career) carried the shock of the new, the Louis Vuitton Foundation is a work of confident maturity that amazes with its sheer virtuosity. You can see what is holding it all together – great steel and laminated timber beams and struts, and subtly curved glass – but it still seems scarcely possible. That, as Arnault might well remark to himself, is engineering. This is a vanity project of course, but a very fine one indeed.

Hugh Pearman is an architecture critic.