Savate
Savate is a really cool art, and there is really much more to it than just kicking and punching.
Savate is really the over-all term for the fighting arts of france. Just like in Kali/Eskrima, where arts like panantukan, pananjakman, and dumog come under the kali/eskrima flag, boxe-francaise, la canne, and lutte parisienne come under the savate flag.
What we call savate is actually “boxe-francaise.” It’s the kickboxing aspect of the art, but nothing like kickboxing or TKD. I’ll get more into that later. But, basically, it’s the “sport” aspect of the art. Just like in bjj, where there is sport-jujitsu (no striking), and there is vale tudo (pretty much nhb).
Then there is lutte parisienne, which is the more free-fighting form of the art. Very street-oriented, with lots of throws, kicks from the ground, hair-pulling, eye-gouging, etc. REALLY nasty stuff, from what I’ve experienced.
Then there is la canne, which is the cane-fighting system of france. The movements are based primarily on sabre movements. I have very little experience with this art, and what I have experienced from it is mostly sport-oriented.
The mechanics of a savate kick is really different from tkd or kickboxing kicks. The mechanics are almost identical to muay thai’s, but with this distinct difference: instead of kicking with the shin, they kick with the tip of their shoe.
So, imagine a thai kick with pin-point precision. That’s a savate kick. Not flashing looking, and really not powerful looking. But when it hits you, you feel like throwing up an organ.
Best thing you can do is experience the art for yourself. Spar with a savateur. You’ll get a better appreciation of the art that way.
As for how it fits into JKD…they work with the same concepts and principles. But I don’t have time to really map that all out. 
Good luck, and hope this helps.
Never confuse sparring with fighting. One is an exchange of skill; the other an exchange of blood.