The French irritated by English game (8)
I believe the answer is:
lacrosse
'game' is the definition.
(lacrosse is a kind of game)
'the french irritated by english' is the wordplay.
'the french' becomes 'la'.
'irritated' becomes 'cross'.
'by' says to put letters next to each other.
'english' becomes 'e' (abbreviation).
'la'+'cross'+'e'='LACROSSE'
(Other definitions for lacrosse that I've seen before include "Sport played with sticks" , "Like thirteen of the other clues in the French" , "Score's uncertain after the Spanish" , "Game played with nets on sticks" , "Game played with netted sticks" .)