From Old French 'bouton' (knob, bud), from 'bouter' (to push) — literally 'a little pusher.'
A small disc or knob sewn on to a garment to fasten it by being pushed through a buttonhole.
From Old French bouton (a button, bud, knob, small protuberance), the deverbal noun from bouter (to push, to thrust forward, to strike against), from Frankish *bōtan (to beat, to push, to strike), from Proto-Germanic *bautaną (to beat, to push, to strike), related to PIE *bʰewdʰ- or an extended *bhāut- root meaning to strike. A button is literally a pusher — something designed to push through a buttonhole, or conversely something that pushes outward like a plant bud. Old French bouton meant both the fastener and a plant bud, and both senses entered Middle English
In French, 'bouton' means both 'button' and 'bud' — both are small knobs that push outward. 'Debut' is literally 'from the push' — a first appearance, a first push onto the stage. 'Rebut' is to push back. A 'buttress' pushes against a wall. And a 'boutique' was originally a 'pushing-place' — a workshop where things were produced (pushed out). All from the same push.