As far as I can tell savate when it was create by casseux was already an existing style or at least is a conjunction of existing style (be it chausson or wrestling).
The idea of savate was to wear shoes when using it.
From it early day it was designed to be used in conjunction with the cane or any weapons, so originally it seems that it was not a kicking art per see but the kicking bit or a bigger art.
On the medival bit
As far as I can tell ringeck is the only to mention punch (well potential punch)
Greyff den man an mitt der lincken hand ober der gürtel, wo du wilt. Domitt stoß in mitt diner gerechten hand zugeschlossene (73 v )mitt kröfften ansin hertz. Do mitt greyff ain ringen, so es dir beste werden mag
Grab the man with the left hand above the belt, where you whish/want. At the same time with the hand appropriately (gerechten substantive form of gerechter ?) /or right hand closed/locked strike at his heart. With that grab him with a wrestling you may think is the best
Der dritt mort stoß.
Greuff den man an mitt der lincken hand ob der gürtel; vnd schlach inmitt gerechten hand zu geschlossen an den schlauff, so du hertest magst;vnd domitt ain starck ringen vff din bestes.
Grab/attack the man with the left hand above the belt, and strike him with the hand appropriately (gerechten substantive form of gerechter ?)/right hand closed/locked in the temple (slaf= Schläfe) or (schluf=soft and stinky= nose or mouth ?). As hard as you can and with that wrestle strongly onto your best.
Ain mort stoß.
A murder stroke
Stoß in mitt baiden fernnsten henden zu geschlossen, so du härtest magst,an den halß. Darnach ring.
Stike/move at him with the furthest of both/either hands closed, so that you may be at the hardest at the neck after that wrestle.
That is pretty much open hand strike with hand closed.
There is only the knee in the goolies in the out of armour wrestling.
In armored wrestling you can kick the knee. Front kick or side kick he does not precise. And straight kick or knee in the gonads however we are warned to be careful that he does not grab us.
One Ringeck to bring them all and in darkness bind them,
In the Land of Windsor where phlip phlop live.