Cheese from France went bad on a regular basis (4)
I believe the answer is:
feta
'cheese' is the definition.
(I know that feta is a type of goat cheese)
'france went bad on a regular basis' is the wordplay.
'france' becomes 'f'.
'on a regular basis' indicates alternate letters.
'went'+'bad'='wentbad'
The alternate letters of 'wentbad' are 'eta'.
'f'+'eta'='FETA'
'from' is the link.
(Other definitions for feta that I've seen before include "Eastern Mediterranean cheese" , "Greek cheese from goat or sheep milk" , "White Greek cheese" , "Greek dairy product" , "food there" .)