Young woman's mother the French brought back (6)
I believe the answer is:
damsel
'young woman's' is the definition.
(damsel is a kind of young woman)
'mother the french brought back' is the wordplay.
'mother' becomes 'dam' (female parent of an animal).
'the french' becomes 'les' (les is the in french).
'brought back' says the letters should be written backwards.
'les' back-to-front is 'sel'.
'dam'+'sel'='DAMSEL'
(Other definitions for damsel that I've seen before include "Young single woman" , "Old-fashioned young woman" , "Young woman (often in distress)" , "Girl (literary)" , "Maiden (poetic)" .)