“My main focus is on creating a program because our collections are so varied,” says Mr. Whitmore, who has 100 exhibitions of various sizes on display around the world. For example, the museum’s “Cult of Beauty” exhibition on the Aesthetic Movement (until July 17) will move to the Musée d’Orsay in Paris in September and on to the de Young in San Francisco next February.

The Musée des Arts Décoratifs is, like the V&A, a decorative arts museum, although that even includes Ralph Lauren’s vintage car collection (until Aug. 28), which Ms. Salmon says is about the art and craft of the automobile.

Ms. Golbin, who joined the museum in 1993, has produced exhibitions on fashion as varied as Balenciaga and Viktor & Rolf, said, “I know what can work. It has to be strong enough from design point of view.”

Her next exhibition, after Chalayan, is already raising eyebrows: Louis Vuitton and Marc Jacobs. Ms. Golbin sees a story about the industrialization of the 19th century followed by the globalization of the 20th. Others might read it as pure promotion.

Ms. Salmon says the 2012 exhibition will reflect the museum’s attitude, drawing around 50 percent of the items from its own archives of Louis Vuitton leather bags and trunks. The Jacobs material will come from Vuitton, which will be the show’s sponsor, just as the Alexander McQueen exhibition in New York is sponsored by the house of McQueen, part of the PPR luxury empire.

The subject of sponsorship is delicate. With all museums short of money, almost no fashion exhibition could take place without some external investment. Mr. Saillard is even frustrated that sponsors — in fashion or art — are drawn always to the same big museum names and that wealthy brands do not try to help museums with funding, even though their creative teams do research there. To the curator’s chagrin, luxury groups like LVMH Moët Hennessy Louis Vuitton and PPR are investing in contemporary art projects, rather than in museum fashion.