Faubourg is not French for "the district." It is a contraction of "faux bourg", French for "false town" and were used to designate smaller towns attached to larger towns or cities. A lot of these faubourgs were independent cities until they were attached to Paris and lost all independence around during the 17th and 18th century. A new outer wall was later erected around the city. These faubourgs, especially those on the East side, were usually blue collar, with a very active night life.
The old man, Monsieur TSF, who stays in his apartment is named after the original French name for radio: "Telediffusion Sans Fil", which means "Wireless Broadcasting" in French, abbreviated "TSF".