Soon to receive a no from the French (4)
I believe the answer is:
anon
'soon' is the definition.
(synonyms)
'to receive a no from the french' is the wordplay.
'to receive' indicates putting letters inside.
'from the french' becomes 'an' (I can't justify this - if you can you should give a lot more credence to this answer).
'no' inserted inside 'an' is 'ANON'.
Can you help me to learn more?
(Other definitions for anon that I've seen before include "Well-published writer" , "soon to be written" , "Soon, precious stone" , "prolific author" , "In a little while (informal)" .)