It's the first Sunday of the month, so don't forget that a number of national and municipal museums offer free entry. You can find a full list of these museums here.
Paris Face Cachée
I interviewed the organisers of this event, which looks to be fascinating, on Invisible Paris, but no sooner was it published than it was apparently sold out. Aiming to show both visitors and locals alike a hidden side of one of the most well-known cities in the world through a series of 'experiences', it may be a victim of its own success, but keep an eye on their website to see if any last minute places become available. With the artic temperatures, there is a good possibility that people will cancel their visit, freeing up space for others.