Because I went around and saw it after drinking the coffee, the Fashion Museum was a mistake. The museum is not very big, the exhibits are relatively fashionable, and are relatively close to the cutting edge of the trend. It is a very interesting museum, and there are not too few people visiting it.
France is the fashion capital. If you have time, you should visit the fashion museum to experience the fashion of the fashion capital.
Popular museum for cloth
If you can catch this museum when it is open, it has fascinating fashion expos. from July - October 2014, there is an exhibit on 50s fashion starting right after the end of WWII, and including a plethora of fashion designers such as Jacques Fath, Jacques Heim, Christian Dior, and tid bit of Channel.
Beautiful, small (?) palace in the 16th. I saw the 100 Years of Conde Nast Fashion Photography exhibit there, and it was beautifully done (May 2014). A nice area to stroll around, make your way to the fancy hotels, and have an expensive cocktail. Fair warning that almost nothing else is open on Sundays in that area.