"young domestic cock" (up to 1 year old), mid-15c. (late 12c. as a surname), apparently a diminutive of cock (n.1). Despite the form, no evidence that it is from French.
Entries linking to cockerel
"male of the domestic fowl," from Old English cocc "male bird," Old French coc (12c., Modern French coq), Old Norse kokkr, all of echoic origin. Compare Albanian kokosh "cock," Greek kikkos, Sanskrit kukkuta, Malay kukuk. "Though at home in English and French, not the general name either in Teutonic or Romanic; the latter has derivatives of L. gallus, the former of OTeut. *hanon-" [OED]; compare hen.
Old English cocc was a nickname for "one who strutted like a cock," thus a common term in the Middle Ages for a pert boy, used of scullions, apprentices, servants, etc. It became a general term for "fellow, man, chap," especially in old cock (1630s). A common personal name till c. 1500, it was affixed to Christian names as a pet diminutive, as in Wilcox, Hitchcock, etc.
A cocker spaniel (1823) was trained to start woodcocks. Cock of the walk "overbearing fellow, head of a group by overcoming opponents" is from 1855 (cock in this sense is from 1540s). Cock-and-bull in reference to a fictitious narrative sold as true is first recorded 1620s, perhaps an allusion to Aesop's fables, with their incredible talking animals, or to a particular story, now forgotten. French has parallel expression coq-à-l'âne.
Cock-lobster "male lobster" is attested by 1757.
The cock-lobster is known by the narrow back-part of his tail; the two uppermost fins within his tail are stiff and hard, but those of the hen are soft, and the tail broader. The male, though generally smaller than the female, has the highest flavour in the body; his flesh is firmer, and the colour, when boiled, is redder. [Mrs. Charlotte Mason, "The Ladies' Assistant for Regulating and Supplying the Table," London, 1787]