Hi!
Just putting my 0.02 €... I wouldn't say Patricia Kaas is very popular in France. People know her name still because she had two smash-hits (
Mademoiselle chante le blues and
Les Hommes qui passent) but she dropped out of hearing a while ago... I think she went straight from "smash-hit on heavy radio rotation" to "oldie but goldie"... now you can hear her songs only on "oldies" radio stations and tv shows (e.g. "Radio Nostalgie"). But I keep hearing about her making it big in other countries, so good for her
As for other French (or French-speaking) singers or bands, I can name a few...
The "old guard" (and the dead ones -- r.i.p.): Boris Vian, Georges Brassens, Jacques Brel, Barbara, Yves Montand, Eddy Mitchell, Charles Aznavour, Bernard Lavilliers, Renaud, Jacques Higelin
Rock: Jean-Louis Aubert (former singer of the band "Téléphone" -- now defunct), Noir Désir, Weeper's Circus, Les Négresses Vertes, De Rien, Louise Attaque...
"Singers/songwriters": Jeanne Cherhal, Brigitte Fontaine, Thiéfaine, Arno, Miossec, Les Têtes Raides, Yann Tiersen
Heavy/Fusion: Trust, Assassins
Rap / R'n'B: IAM, MC Solaar
This is by no means a full list, but you have a good few names to start with
