Shoot French author's son in the head (6)
I believe the answer is:
sprout
'shoot' is the definition.
('sprout' can be a synonym of 'shoot')
I don't understand the rest of the clue.
(Other definitions for sprout that I've seen before include "Put out shoots for the vegetable" , "Start growing" , "Begin to develop" , "Push out new shoots" , "Young shoot" .)