"pustule raised on the surface of the body in an eruptive disease," Middle English pok, from Old English pocc "pustule, blister, ulcer," from Proto-Germanic *puh(h)- "to swell up, blow up" (source also of Middle Dutch pocke, Dutch pok, East Frisian pok, Low German poche, dialectal German Pfoche), from PIE root *beu- "to swell, to blow" (see bull (n.2)).
French pocque is from Germanic. The plural form, Middle English pokkes "disease characterized by pustules" (late 14c.) is the source of pox.
"to disfigure or mark with pustules or the pits left by them," 1841 (implied in pocked), from pock (n.). Related: Pocking.