Every first Sunday of the month all the national museums are free, permanent collections as well as temporary exhibitions. Aside from those museums you can also visit, for FREE and at ANYTIME, the PERMANENT COLLECTIONS of the MUNICIPAL(city-run) MUSEUMS, such as the Musée d’Art Moderne , Maison de Balzac , Musée Bourdelle , Musée Carnavalet , Musée Cernuschi , Musée Cognacq-Jay , Musée du Petit Palais , Maison de Victor Hugo , Musée de la Vie Romantique , Musée Zadkine , Pavillon de l’Arsenal  and Le Plateau .
So, admission to Paris municipal museums is free for all, except for the temporary exhibitions as well as the Catacombes, Notre-Dame’s Crypte, the Musée des Egouts and Musée Galliera.
Please note that all the municipal museums are closed on holidays (January 1st, Easter Sunday, May 1st, May 8th, Ascension, Pentecostal Sunday, July 14th, August 15th, November 1st, November 11th, December 25th.)
Also, a small window of free access in the following museums:
La Maison Européenne de la Photographie  offers free admission on Wednesday from 5pm-8pm.
Le Musée des Arts et Métiers  offers free admission on Thursday from 6pm-9.30pm.