Lady of the French game (7)
I believe the answer is:
duchess
'lady' is the definition.
(duchess is a kind of lady)
'of the french game' is the wordplay.
'of the french' becomes 'du'.
'game' becomes 'chess' (chess is a kind of game).
'du'+'chess'='DUCHESS'
(Other definitions for duchess that I've seen before include "Titled lady" , "title" , "Duke's wife" , "Noble lady" , "Great lady" .)