Where does “coite” come from?

coite (Old French) comes from Latin culcita, from Proto-Indo-European kʷel- — to turn.

Ancestry of “coite”, step by step

Step	Language	Word	Meaning
1	Latin	culcita	mattress, pillow, cushion
2	Proto-Indo-European	kʷel-	to turn

coite — Etymology, Origin & Word History | Etymology Explorer