Dreadful, the French record (9)
I believe the answer is:
chronicle
'record' is the definition.
(chronicling is a kind of recording)
'dreadful the french' is the wordplay.
'dreadful' becomes 'chronic' (old-fashioned slang for 'poor quality').
'the french' becomes 'le'.
'chronic'+'le'='CHRONICLE'
(Other definitions for chronicle that I've seen before include "Continuous record of events in order of time" , "Narrative description of past events" , "Account of important events" , "journal" , "(Keep an) historical record" .)