Puss has swallowed part of the French cheese (9)
I believe the answer is:
camembert
'the french cheese' is the definition.
(I've seen this before)
'puss has swallowed part' is the wordplay.
'puss' becomes 'cat' (I've seen this in other clues).
'has swallowed' is an insertion indicator.
'part' becomes 'member' (member is a kind of part).
'cat' placed around 'member' is 'CAMEMBERT'.
'of' acts as a link.
(Other definitions for camembert that I've seen before include "Soft rich cheese as made in Normandy" , "French produce" , "Soft creamy French cheese" , "For something to eat" , "French food" .)