Irritate the French following row (6)
I believe the answer is:
rankle
'irritate' is the definition.
(rankling is a kind of irritating)
'the french following row' is the wordplay.
'the french' becomes 'le'.
'following' is a charade indicator (letters next to each other).
'row' becomes 'rank' (I've seen this before**).
'le' after 'rank' is 'RANKLE'.
(Other definitions for rankle that I've seen before include "Cause lasting annoyance or resentment" , "get someone's goat" , "Cause continuing irritation" , "Cause lasting bitterness or upset" , "Continue vexing" .)