I am a native Romanian, a Romance language with a lot of French neologisms that resulted in many (more or less) false friends. Thus, I was very surprised in France to hear people saying about a girl with light skin and brown hair that she was "une jolie brune". — The French brunet has given an identical term in Romanian and brunette has given the word brunetă, both meaning people with somewhat dark skin and hair, and usually dark-colored eyes, something like the "Mediterranean" type, let's say George Clooney and Claudia Cardinale

but surely not simply people with brown, dark-brawn or black hair.

CNRTL says about brunette:

A.− Emploi adj.
1. Rare. Légèrement brun(e), tirant sur le brun. ...
2. P. méton. [En parlant de pers.] Dont les cheveux tirent sur le brun...

B.− Emploi subst.
1. Jeune femme, jeune fille dont les cheveux sont bruns, tirent sur le brun. 

And is there a term for people with fair skin and black hair?