Translating the word 'brown' when applied to hair colour?

Peter : 

«The colour brun is defined as a dark red going on black (Dictionnaire de l'Académie française).
In colloquial French, brun will mostly be used to describe hair, skin (as in tanned skin), or fur.
In other cases, we will use marron. »

"Brun" can and is used for hair/fur/skin colour - but it is not the direct equivalent of the English 'brown'. 

As for the reason that 'marron' is used, it is usually best not to ask 'why' questions of usage and grammar as the answer is mostly 'because'. In this case, however, I think at least in part that is also covered in the lesson - in French «brun» and «marron» (and bordeaux) define different shades of 'reddish-brownish-blackish', and have different meanings to the English 'brown' and 'maroon'. (Colour descriptions by name are always subjective in any language -  international colour standards do not use names, they use digital systems).