The FEW proposes pungere as the etymon, which groups this noun with poindre1 (‘to prick, pierce, stab’). However, it confirms (9,600a n.9) that this noun may also be derived from the verb pugnare (‘to engage in single combat, to fight, wrestle’ DMLBS 2565c), although, it claims, vernacular derivatives of this verb are rare. Semantically, a small group of words, centred around poigne1 (from pugna, ‘battle’) seems to have existed in Anglo-Norman.

As the OED suggests, because of the formal and semantic overlap, a further association of the word-group with poin1 (‘fist’), from Latin pugnus, seems likely (etymology of poynye n.).