French word picoter comes from French -oter, French piquer

Detailed word origin of picoter

Dictionary entry	Language	Definition
-oter	French (fra)	(colloquial) Forming verbs from other verbs, with a diminutive or frequentative sense.
piquer	French (fra)	(colloquial) to nick, pinch, steal. (reflexive) to pride oneself on; to like to think that one can do (+ de). (textiles, couture) to stitch together. To prick (pierce with a prick). To sting (feel a stinging pain).
picoter	French (fra)	(informal) to bug, to pester, to annoy. (of a bird) to peck. To itch, to prickle. To tingle.

Words with the same origin as picoter