On the other hand, the OED2 says
A name app. of English invention: either originally intended, or soon after assumed, to represent a supposed Fr. *corde du roi ‘the king’s cord’; it being a kind of ‘cord’ or corded fustian.
No such name has ever been used in French: on the contrary, among a list of articles manufactured at Sens in 1807, Millin de Grandmaison Voyage d. Départ. du Midi I. 144 enumerates ‘étoffes de coton, futaines, kings-cordes’, evidently from English. Wolstenholme’s Patent of 1776 mentions nearly every thing of the fustian kind except corduroy, which yet was well known by 1790. Duroy occurs with serge and drugget as a coarse woollen fabric manufactured in Somersetshire in the 18th c., but it has no apparent connexion with corduroy. A possible source has been pointed out in the English surname Corderoy.]
You pays your money and you takes your chances.
Possibly relevant to the last suggestion in the OED, all the pre-1800 cites use the spelling “corderoy”; the -u- was apparently a later modification.
And I don’t know where etymonline (at Oeco’s “this” link) gets the notion that it originated as American English.