Store of French lassi, outside (4)
I believe the answer is:
deli
'store' is the definition.
(deli is a kind of store)
'of french lassi outside' is the wordplay.
'of french' becomes 'de'.
'outside' suggests removing the centre.
'lassi' with its middle taken out is 'li'.
'de'+'li'='DELI'
(Other definitions for deli that I've seen before include "food-store?" , "Food shop (abbr)" , "small food shop" , "Specialist foodshop(abbr.)" , "food outlet" .)