The Paris Exception
Gites are officially rural homes, though in practice, many are quite near, or in the heart of major French towns. You will not find any in Paris, however, so for the City of Light, you'll need to consult with an apartment broker. As with gites, the costs for weekly stays will usually be considerably less than you'd pay at a hotel (especially if you factor in the savings of being able to cook for yourself).
The full-service agency Parisian Home (www.parisianhome.com), has a wide range of options, including a number of quite affordable digs. Appartmente de Ville (www.appartementdeville.com), another full-service outfit, is known for the quality of its luxe apartments. For real penny pinchers, I recommend Allô Logement Temporaire (www.allo-logement-temporaire.asso.fr), a non-profit association which puts private owners in touch with would-be-renters. It's less hit or miss than other direct-to-owner sites for Paris, as its staff does do some oversight.