The personal name Jacques supplied a peasant term, then jaque for a short jacket. The diminutive plural jackés passed into Middle English as jaket.
The earlier personal name Jacques is explained here but not duplicated as a card that differs only in capitalization.
Sources
- Merriam-Webster: jacket
Middle French jacques, peasant, precedes jaque, the diminutive plural jackés, Middle English jaket and modern jacket.
- Anglo-Norman Dictionary · jaket
Meanings of the older forms on the word path.
- Online Etymology Dictionary · jacket
Meanings of the older forms on the word path.