In looking the word up in my dictionary, the etymology mentioned "savate" which I have
not heard for a long time.
savate
n.
5Fr, orig., old shoe: see SABOT6 a form of boxing in which stiff-legged kicks as well as punches
may be used

WWI doughboys got some "kicks" out of French gendarmes, quite literally.
They came home with a little ditty: "The French they are a funny race, The fight with their feet,
and fxxx with their face." Much later many Americans adopted view "40 Million Frenchmen
can't be wrong."