Yeah, TTC are great. Everyone should listen to em whether or not they can understand the words.
I'll suggest Brigitte Fontaine. She's like the French 60s equivalent of, say, Patti Smith or Yoko Ono. But better than both. She collaborated with Art Ensemble of Chicago. Sort of folk, ethnic stuff - her most out-there music verges on Volcano the Bear/This Heat territory. Some of her stuff is extremely funky. Anyone who likes, say, Bat For Lashes or Joanna Newsom (I hate both) ought to listen to Brigitte Fontaine to hear how it should be done.
I also like Pierre Barouh. he's like the French Leonard Cohen. He was mates with Brigitte Fontaine. He played quite a lot of bossa nova stuff.
Boris Vian is my favourite French musician. On a big band jazz tip. He was a surrealist who wrote the noir novel I Spit on Your Grave. He was a jazz fiend and organized tours for Duke Ellington and the like in Europe. His lyrics are brill, and he vociferously opposed the Algerian war. He satirised the bourgeoisie (and himself) whenever he could. Great tunes too.