As there's currently not much good music sung in French I'll make a list of albums worth checking out from any period:
Serge Gainsbourg - Jane et Serge / Histoire de Melody Nelson
Françoise Hardy - Comment te dire adieu / La question
Brigitte Fontaine - Brigitte est... / Comme à la radio / S/T / Vous et nous
Alain Bashung - Fantaisie militaire
Dominique A - La mémoire neuve / L'horizon
Jean-Louis Murat - Dolorès / Mustango
You should be able to listen to songs from those albums on
http://www.jiwafm.fr/fr or
http://www.deezer.com/