The French head of air force permits flyers (8)
I believe the answer is:
leaflets
'flyers' is the definition.
(I know this)
'the french head of air force permits' is the wordplay.
'the french' becomes 'le' ('the' in French).
'head of' suggests taking the first letters.
'permits' becomes 'lets' ('let' can be a synonym of 'permit').
The initial letters of 'air force' is 'af'.
'le'+'af'+'lets'='LEAFLETS'
(Other definitions for leaflets that I've seen before include "Printed sheets" , "Flyers" , "Little growth" , "fliers" , "Pamphlets giving information, often to advertise" .)