But there is, and it's not your average museum either: the National centre for stage costumes - and stage sets/décors, offering exhibitions, workshops and other events, all related to the stage and performance - the theatre, opera, ballet, etc.
The museum is housed in former military cavalry barracks dating from the end of the 18th century and classified as a historical monument.
Have a look around their site, there are videos with such people as fashion designer Christian Lacroix and more, very interesting!: CNCS
I went there this week to see their current exhibition, "L'art du costume de la Comédie-Française". In France, la Comédie-Française is the equivalent of the Royal Shakespeare Company in terms of prestige. We saw wonderfully made costumes that had been worn by some of the greatest French stage actors, from the 18th century to the present.
If you want to know more about the exhibition, you can find a French version of the blurb here:
COMEDIE FRANCAISE EXHIBITION ENGLISH VERSION