The late '90s through naughts brought forth a really solid range of extreme horror from France, most notably in the form of High Tension, Frontier(s), Martyrs, and my personal favorite, Inside (which is 10 years old, a fact which helps me cry myself to sleep at night).
What I love about Inside is the way it captures the horror both in being alone and in being a pregnant woman, as well as the emotional and physical vulnerability of that physical state. There's also a great little twist about her attacker and an admirable level of gore. There are problems with it, as there seem to be with all extreme horror from the land of wine and cheese. Some of the additional scenes of violence feel a little tacked on for the sake of that sweet gruesome excess, for example. Nonetheless, I still count it among my favorite films.
A more recent, slightly less extreme outing that I'd still place under this banner is Raw, which I got a chance to see at Sundance this year. While it's not filled to the brim with blood and guts, it still features many of the bonkers plot elements, disturbing imagery, and social commentary that I expect from the sub-genre.
There are of course less extreme French horrors (Eyes Without a Face, With a Friend Like Harry...), but I'd love to know what your favorite EXTREME French horror flick is!