I looked at the link you provided. This group definitely represents the Good Guys, and is explicitly opposed to the spirit of the French Revolution and, thus, the founding principles of the current secularist republic. The symbol of the Sacred Heart that the group uses is the exact same as used by the Vendée counter-revolutionaries.
No wonder the government hates them.
Is it the same group? I don't speak French so I couldn't determine whether they are or not. Perhaps they are a splinter group off another order?