IIRC - the french/Paris has a special force for riots, big, mean guys that do not ask questions or make requests, they were the ones the could not get into the police dept for various reasons but were big and nasty.
Foreign Legion?
Those are part of the Special Gendarmerie, usually attached to the anti-terrorism forces and like you said riot suppression
Watched them in action during the Uber riots
Big cat and mouse game between them and the unionistas
This is why Paris has very wide boulevards. Before Napoleon 3rd and Haussmann, Parisians created choke points and blocked off streets to police.