Girl embracing very French lover (8)
I believe the answer is:
mistress
'lover' is the definition.
(I've seen this before)
'girl embracing very french' is the wordplay.
'girl' becomes 'miss' ('miss' can be a synonym of 'girl').
'embracing' indicates putting letters inside.
'very french' becomes 'tres' ('very' translated into French).
'miss' enclosing 'tres' is 'MISTRESS'.
(Other definitions for mistress that I've seen before include "lover" , "Woman teacher" , "Woman in control" , "Female teacher" , "Lady" .)