Take a look at a site such as HomeAway.com, which includes rental listings by local property owners in cities around the world, including Paris. Once you find a place you like, you coordinate with the owner directly and put down a deposit, typically between 10 to 50 percent. HomeAway is currently listing a really nice looking two-bedroom apartment near Sacre Couer and Montmatre (http://www.homeaway.com/vacation-rental/p224052) for about $1,500 per week in the summer high season (so about $200/night). Not a bad rate for somewhere with all the comforts of home. Other similar sites you might try include Airbnb.com (a little more "homestay"-ey) or iStopOver.com.