Vegetable popular primarily in South of France (4)
I believe the answer is:
spud
'vegetable' is the definition.
(spud is a kind of vegetable)
'popular primarily in south of france' is the wordplay.
'primarily' suggests taking the first letters.
'in' indicates putting letters inside.
'south of france' becomes 'sud' (French for south).
The initial letter of 'popular' is 'p'.
'p' going inside 'sud' is 'SPUD'.
(Other definitions for spud that I've seen before include "The common potato" , "one's eyed" , "Weed spade" , "short, stocky person" , "Weeding spade" .)