Crossword Genius

French writer has son going back for shoot (6)

Ross

I believe the answer is:

sprout

I'm a little stuck... Click here to teach me more about this clue!

'shoot' is the definition.
(synonyms)

'french writer has son going back for' is the wordplay.
I cannot quite see how this works, but
'son' could be 's' and 's' is present in the answer.
'for' could be 'pro' (I've seen this before) and 'pro' is present in the answer.
The remaining letters 'ut' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for sprout that I've seen before include "Produce new growth" , "Young shoot" , "Put out shoots for the vegetable" , "Develop new growth" , "Put out shoots for a brassica" .)

I've seen this clue in The Hindu.
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