My two favorite sights that aren't so famous:
The Museum of Counterfeits, near the Bois de Boulogne. This has not only fake purses, but also more sinister things, like fake medicines and car parts that have caused fatalities. As a bonus, it's at the Porte Dauphine metro stop, one of the few fully intact metro canopies left. The address is 16 Rue de la Faisanderie in the 16th arrondissement.
Their website is only in French, and I see that they are now open Monday to Saturday, but for individuals only in the afternoons (14:00 to 17:30). Admission €6. https://musee-contrefacon.com/infos-pratiques/
The Gobelins Manufacture is having an exhibit on 100 years of tapestries. I had previously not been that enthralled by tapestries, but some of the ones in this exhibit are amazing. Many are done by famous painters in all kinds of styles - impressionist, op art, etc. As technology advanced, they were able to simulate various styles of painting in the tapestries, to the point where from a distance it's impossible to believe you're looking at a carpet. They can really capture the look of a watercolor wash, or paint put on with a palette knife - amazing!
It's at 42 avenue des Gobelins in the 13th arrondissement (metro Les Gobelins). Open 11-8, closed Mondays. Admission €8. Be aware that they have no bag check, and you can't wear a backpack on your back, but must wear it in the front. Website only in French: http://www.mobiliernational.culture.gouv.fr/fr
For the websites, you can use Google Translate if needed.