Savate punches are directly taken from boxing and, although this is predominantly a kicking sport, the ability to use your hands effectively will get you far.
We refer to Savate fighting as boxing, even when we are kicking, and the French even make a distinction by calling boxing (pugilism) boxe anglais. Punching technique in Savate is largely that founded on the Marquis of Queensbury rules (1865-67) and those of the international boxing federations that followed. It is not unusual to use English terms for punches in Savate, while using French words for the kicks, which preserves the split in their origin.
That said, there is an explicit rule which states that boxing (with the hands) cannot predominate over kicking in Savate competition (read more here), and boxing technique scores less well than kicking technique. Nonetheless, boxing is perhaps the most used cross-training for Savate fighters.
List of Savate Punches
The Federation International publishes a rule book which describes legal Savate technique (French language, external link).
Direct
Straight punch, just like a jab or a cross.
Uppercut
Uppercut.
Crochet
Hook.
Example: Direct (straight) Savate punches, demonstrated by head coach James Southwood.