I guess the thing with natural red hair’s that it’s often more of a dull orange or red-brown colour but linguistically the naming varied. It seems in French, Russian, Irish, Polish, Ukrainian and Belarusian and to some extent, Catalan and Portuguese the word for red hair’s distinguished from red in general. (There might be some overlap in which at some point red-brown hair was called rouge acajou.)
But from personal experience, at least recently cheveux rouges pretty much means bright red hair. Actually it’s a colour so red it’s practically pink in some lighting. There are some people who do dye their hair with this colour. Plus I think with wool, though not always the case I get the impression of henna-dyed wool to be a dull orange colour.
(Some) madder-dyed wool being a nice red or pink. It seems parsimonious to say dyed wool can give a good idea of what some human hairs are like if dyed with madder. I still think if natural red hair’s often a dull orange or reddish brown colour, some madder-dyed wool seems like a nice dull pink. (Well if it were a bright red, it would be pink in some lighting.)