Twice this year I stayed at a wonderful family-owned apartment in the center of Paris. It is not only cheaper than a hotel room, but it also has a fully equipped kitchenette, a full bath, unlimited free phone calls to the U.S. and free Wi-Fi. It also is a short block from the fantastic market street the Rue Mouffetard.
For information, go to https://www.levieuxparis.com. From $135 a night, depending on the season. Five-night minimum.