Bitterly continue a row with the French (6)
I believe the answer is:
rankle
'bitterly continue' is the definition.
(to rankle can mean to continue to irritate)
'a row with the french' is the wordplay.
'a row' becomes 'rank' (I've seen this in another clue).
'with' is a charade indicator (letters next to each other).
'the french' becomes 'le' ('the' in French).
'rank'+'le'='RANKLE'
(Other definitions for rankle that I've seen before include "Annoy continually" , "Cause continuing irritation" , "Irritate for a long time" , "get up your nose" , "Continue to annoy" .)