Each apartment is individually owned and listed on VRBO.com, and while I can't vouch for all the owners, my landlords in Paris couldn't be more gracious or obliging.
If you're interested in renting the apartment, here's the link. The building is aging and has a few quirks, but the apartment is beyond charming. Here's the link to more pictures on my flickr page.
As you'd expect, the rates are lower in winter, when the airfares are also on special. I flew to Europe on Air France with a last minute deal spotted on their website.
The next place I'd like to go is Barcelona.