Looking for US artists singing French songs I find Rufus Wainwright's interpretation of La complainte de la butte that was initially created by Cora Vaucaire, the voice in the Jean Renoir's film French Cancan and by Mouloudji in 1955.
Lyrics by Jean Renoir Music Georges Van Parys
En me promenant sur YouTube, Noir Désir et Le vent nous portera.
Henri Salvador created many great songs during his long career. I have chosen Jardin d'hiver because it is one of the last he performed. His voice has not aged that much if at all. Listen also to his 2001 rendering of his song Syracuse (1960).