Go back with the French and eye greedily (4)
I believe the answer is:
ogle
'eye greedily' is the definition.
(I've seen this in another clue)
'go back with the french' is the wordplay.
'back' says the letters should be written in reverse.
'with' is a charade indicator (letters next to each other).
'the french' becomes 'le' ('the' in French).
'go' back-to-front is 'og'.
'og'+'le'='OGLE'
'and' acts as a link.
(Other definitions for ogle that I've seen before include "Look at amorously" , "Gape at" , "Eye lewdly" , "Eye flirtatiously" , "Amorous glance" .)