Hopelessness of the French duo (7)
I believe the answer is:
despair
'hopelessness' is the definition.
(despair is a kind of hopelessness)
'of the french duo' is the wordplay.
'of the french' becomes 'des'.
'duo' becomes 'pair' ('pair' can be a synonym of 'duo').
'des'+'pair'='DESPAIR'
(Other definitions for despair that I've seen before include "State of having lost all hope" , "Despondency" , "Complete absence of hope" , "gloom" , "displaying lack of optimism" .)