Aside from hotels, apartment rentals, and bed & breakfast accommodations, there are a few other options to consider:
There are many agencies on the internet that you san sign up with to exchange homes with a Parisian. Sometimes you even get to exchange pets and cars! Of course, this works better if you live in a place where many Parisians want to visit: New York, San Francisco, Miami, London, Toronto, Montreal, Sydney, etc. But you never know, so why not try it? I have no personal experience with any agencies in particular, so I won’t list any links here for the moment (just Google “home exchange”).
You can also try it directly without an agency through websites like Craig’s List Paris or FUSAC (be sure to verify identity and ownership before you do this, please!)
For people who like meeting locals face-to-face, then try the phenomenon known as Couch Surfing. The basic idea is that you get to crash free on someone else’s sofa in return for opening your sofa to potential travelers (not necessarily the same one whose sofa you crashed on).
Another site, one I’ve used (as a host, rather than a guest) is Global Freeloaders. It’s important to note that it doesn’t cost anything to sign up, and people post “reviews” for good guests and hosts (a bit like eBay vendor ratings) to make it a bit more open and safe.
Camping in Paris
Why yes, there actually is a Paris campsite in the Bois de Boulogne (and a second one closer to Disneyland Paris). And if you don’t have your own motorhome/camper/tent, you can even rent one of their bungalows. Not a bad deal for travelers who can’t decide on “city or country”. You can find other French campsites in the region and throughout France onOutCamp.