The French one is slim (4)
I believe the answer is:
lean
'is slim' is the definition.
('lean' can be similar in meaning to 'slim')
'the french one' is the wordplay.
'the french' becomes 'le'.
'one' becomes 'an' (I've seen this in other clues**).
'le'+'an'='LEAN'
(Other definitions for lean that I've seen before include "David ..., director of Ryan's Daughter" , "Meagre" , "Thin; rest (against)" , "Incline; (of person) thin" , "Rest against for support" .)