A French broadcast covering football, primarily, not cricket! (6)
I believe the answer is:
unfair
'not cricket' is the definition.
(I've seen this in another clue)
'a french broadcast covering football primarily' is the wordplay.
'a french' becomes 'un' ('a' in French).
'broadcast' becomes 'air' (to air on TV).
'covering' is an insertion indicator.
'primarily' suggests taking the first letters.
The initial letter of 'football' is 'f'.
'un'+'air'='unair'
'unair' going around 'f' is 'UNFAIR'.
(Other definitions for unfair that I've seen before include "Not equitable-or blonde?" , "Not cricket?" , "Not just - lacking in beauty" , "Weighted" , "raining perhaps?" .)