1650s, "dexterous," originally "rightly," from French adroit, which by Old French had senses "upright (physically and morally); able, clever, skillful; well-formed, handsome; on the right-hand side; veritable," from adverbial phrase à droit "according to right."
This is from Old French à "to" (see ad-) + droit, dreit "right," from Medieval Latin directum (contracted drictum) "right, justice, law," neuter or accusative of Latin directus "straight," past participle of dirigere "set straight," from dis- "apart" (see dis-) + regere "to direct, to guide, keep straight" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule"). It expresses prominently the idea of a trained hand. Related: Adroitly; adroitness.