Corduroy etymology

Solution 1:

To support your speculation, there is the word duroy, pronounced /dəˈrɔɪ/. which was a kind of woolen cloth. The OED mentions this in the etymology section of corduroy, but says it "appears to have no connection to corduroy". However, this might explain why côtelé mutated to cor duroy. This would be especially likely if this mutation took place in a dialect where people dropped their r's, which they seem to have done in London in the late 18th century.

The OED attests the word duroy meaning some kind of fabric from 1722:

London Gazette (1722): Wearing a grey Duroy Coat and Wastcoat.

They also give a 1619 citation, but in that deroy seems to be a color (see the other answer).

The OED's definition of duroy is:

A kind of coarse woollen fabric formerly manufactured in the west of England; akin to the stuffs called tammies. (Not the same as corduroy.)

And duroy does seem like it came from French. The OED gives a quote from a French encyclopedia

Encyclopédie Méthodique (1792): Duroi, étoffe de laine, rase et sèche, dans le genre de la tamise, mais moins large et plus serrée,

which I'm not going to try to translate because these adjectives describing cloth in the 18th century probably don't mean quite the same thing as the same adjectives would in French today.

Solution 2:

According to the following source the often suggested origins of the term like French “cordes du roi” or the English surname “Curdroy” appear to be folk etymologies. A more convincing theory, though not definitive, is the one from “colour de roi”:

The British philologist Ernest Weekley (1865-1954) proposed the most convincing origin in Transactions of the Philological Society (1910):

• Is there not a possibility that corduroy is folk-etymology for the common trade-term colour de roy?

The term colour de roy, which dates from the early 16th century, is from French couleur de roi, king’s colour. It originally denoted a cloth of a rich purple colour associated with the French kings and this colour itself. Later, it also signified a bright tawny colour and a cloth of this colour.

Ernest Weekley mentions that colour de roy occurs frequently in the scholarly editions of primary records of voyages, travels and other geographical material published by the Hakluyt Society. For example, in his diary, Richard Cocks (1566-1624), a merchant venturer living in Japan, wrote, on 26th November 1615:

• The king sent for a bottell Spanish wyne, and desird to buy Mr. Osterwickes cloake, being of culler du roy, which he sent unto hym at price of 20 taies.

(Incidentally, Richard Cocks was one of the first known users of the expression Hobson’s choice.)

Ernest Weekley also cites Randle Cotgrave in A Dictionarie of the French and English Tongues (1611):

• Couleur de Roy, was in old time, Purple; but now is the bright Tawnie, which wee also tearme, Colour de Roy.

And Weekley concludes:

• The ‘bright tawnie’ is the commonest colour for new corduroys, and I imagine it might have been written commercially cᵒʳ de roy. This is, of course, a pure guess.

(Word Histories)