Arguably this can be attributed to strength and rapidity of the German forces in WWII, the French army being largely conscript, the rise of socialism and pacifism. All of which are directly related to the massive losses on both sides during the stalemate of WWI. Essentially a political consequence rather than a reflection of the Frenchmans martial vigor
Essentially though your talking about a time period after the emergence and even the formalisation of savate.
That said, having done some research, savate seems to be a very effective street art but is rendered less effectual without the heavy shoes or boots it gains its name from. Root: sabot, a wooden shoe, ouch.
Savate de rue(of the street) sounds nasty, eye gouges, elbows, grappling, knees and headbutts all included. Also uses stick fighting.
I'd say, Savate de rue, for the street.. and Japanese Kickboxing for sport combat.