Quite drunk on the French drink (7)
I believe the answer is:
tequila
'drink' is the definition.
(tequila is a kind of drink)
'quite drunk on the french' is the wordplay.
'drunk' is an anagram indicator.
'on' says to put letters next to each other.
'the french' becomes 'la' ('the' in French).
'quite' is an anagram of 'tequi'.
'tequi'+'la'='TEQUILA'
(Other definitions for tequila that I've seen before include "Mexican tipple" , "Distilled agave drink" , "Cocktail -- 1988 American crime film -- equaliser units (anag)" , "Liquor made from the agave plant" , "Mexican alcoholic drink" .)