Long-lasting, the French story (9)
I believe the answer is:
chronicle
'story' is the definition.
(synonyms)
'long-lasting the french' is the wordplay.
'long-lasting' becomes 'chronic' (as in chronic illness).
'the french' becomes 'le' ('the' in French).
'chronic'+'le'='CHRONICLE'
(Other definitions for chronicle that I've seen before include "(Make a) historical record" , "Record of historic events" , "Register of events over time" , "Story" , "journal" .)