While having had a very French upbringing, you say (6)
I believe the answer is:
assert
'say' is the definition.
(I know that say is a more specific form of the action assert)
'while having had a very french upbringing you' is the wordplay.
I cannot really see how this works, but
'while' could be 'as' (eg 'while I walked' means 'as I walked') and 'as' is located in the answer.
The remaining letters 'sert' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for assert that I've seen before include "State authoritatively" , "State categorically" , "Aver, maintain" , "Declare or affirm" , "Declare, state vigorously" .)