Hopelessness of the French couple (7)
I believe the answer is:
Here is my best explanation:
'hopelessness' is the definition.
(despair is a kind of hopelessness)
'of the french couple' is the subsidiary indication.
'of the french' becomes 'des'.
'couple' becomes 'pair' ('pair' can be a synonym of 'couple').
(Other definitions for despair that I've seen before include "Despondency", "State of having lost all hope", "Lose heart", "Be without hope", "Opposite of 10", "The complete absence of hope", "Praised (anag) - lose hope", "Total loss of hope", "The feeling that nothing will turn out well" and "Resignation".)