What material comes from the French phrase meaning "the cloth of kings"?

Maybe corduroy (corde du roi"), though the etymology is disputed and the phraes doesn't seem to have been used in French.

That etymology does seem to fit like a good pair of corduroys, TT, but you are right. The OED says that it derives from an old fabric just called "duroy". Mind you, it doesn't say where that took its name from.

I've found a number of fabrics called the "cloth of kings" but corduroy is the only one that seems to come from a French phrase meaning cloth of kings, whether is actually does or not.
https://en.wikipedia.org/wiki/Corduroy

This magnificent material, silk, became known at the "cloth of kings."
http://www.suekayton.com/Silkworms/history.htm

Kente cloth is known as the "cloth of kings" because originally it was made for kings, queens, chiefs, and their royal courts to wear on special occasions.
http://wol.jw.org/en/wol/d/r1/lp-e/102001685

Woven damask is called the "Cloth of Kings."
[califmall.com/rafnel/rafartist.html] - Link no longer valid