French cheese injected with British sweetener (5)
I believe the answer is:
bribe
'sweetener' is the definition.
(sweetener can mean a bribe)
'french cheese injected with british' is the wordplay.
'french cheese' becomes 'brie' (I've seen this before).
'injected with' indicates putting letters inside.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'brie' enclosing 'b' is 'BRIBE'.
(Other definitions for bribe that I've seen before include "Corrupt payment" , "Dishonestly persuade" , "Carrot" , "Square" , "Illegal incentive" .)