For the quintessential french balladeur accompanying himself (mostly) with a classical guitar, I suggest Georges Brassen. He has a deep baritone voice, but not rough as the russian example provided by the OP. His lyrics are extremely poetical, with a vein more lyrical than political, but some social concerns with an anarchist influence are also present.
There are many many french singers cultivating a somewhat similar type of voice, within the aestethics and reportoire of the "Chason Française". Some of the most well known are for example Yves Montand, Serge Regianni, Gilbert Bécaud or Serge Gainsbourg (of "Je T'Aime Moi Non Plus" fame).
A somewhat more politicized figure is Georges Moustaki, who often sung with only his guitar. But his voice is a velvety tenor, far from the rough voice examples of the OP.
Finally, even leaving many names without mention, it would be impossible in this context not to refer Jacques Brel, whose theatrical (some times histrionic) interpretations are perhaps without parallel.