Game with rake capturing the French better's heart (8)
I believe the answer is:
roulette
'game' is the definition.
(roulette is a kind of game)
'rake capturing the french better's heart' is the wordplay.
'rake' becomes 'roue' (both can mean an immoral man).
'capturing' means one lot of letters goes inside another.
'the french' becomes 'le'.
'heart' means to look at the middle letters.
The middle of 'better' is 'tt'.
'le'+'tt'='lett'
'roue' going around 'lett' is 'ROULETTE'.
'with' acts as a link.
(Other definitions for roulette that I've seen before include "Form of gambling" , "Spinning-wheel game" , "SPORT/GAME" , "Half of 1D [GAME OR BIRD]" , "Wheel of fortune" .)