It opens Tues to Sunday from 10am to 6pm but closes on public holidays. The museum is also exceptionally closed on 18 and 19 March 2014 for construction works.
Another free museum in Paris, but less well known, is the Fragonard Perfume Museum, located close to Opera. Here you can discover a large number of perfumery objects throughout the ages with a free guided tour. The museum is housed in a glorious Napoleon III townhouse, which is worth visiting in its own right. It is open everyday from 9am to 6pm (5pm Sun).
A whole host of other museums are free for under 26 year olds from the EU and a number of the most popular Paris museums, such as the Orsay and Pompidou Centre, open their doors for free on the first Sunday of the month. This does make this day extremely popular and so large queues can form. It should also be noted that the Louvre museum is planning to stop free entry on a Sunday during the high season.
Details of these and other museums can be found on the Guide2Paris guide to free museums in Paris.