Prolonged the French narrative (9)
I believe the answer is:
chronicle
'narrative' is the definition.
(I've seen this in another clue)
'prolonged the french' is the wordplay.
'prolonged' becomes 'chronic' (similar in meaning).
'the french' becomes 'le' ('the' in French).
'chronic'+'le'='CHRONICLE'
(Other definitions for chronicle that I've seen before include "Story" , "(Keep an) historical record" , "History" , "Record of historic events" , "Historical account" .)