The French going after instant sea food (6)
I believe the answer is:
winkle
'sea food' is the definition.
(winkle is a kind of sea food)
'the french going after instant' is the wordplay.
'the french' becomes 'le'.
'going after' is a charade indicator (letters next to each other).
'instant' becomes 'wink' ('wink' can be a synonym of 'instant'**).
'le' after 'wink' is 'WINKLE'.
(Other definitions for winkle that I've seen before include "Marine snail" , "Edible shellfish" , "Gastropod" , "Small mollusc" , "Spiral-shelled mollusc" .)