Hopelessness of the French demeanour under pressure (7)
I believe the answer is:
despair
'hopelessness' is the definition.
(despair is a kind of hopelessness)
'of the french demeanour under pressure' is the wordplay.
'of the french' becomes 'des'.
'demeanour' becomes 'air' (air is a kind of demeanour).
'under' says to put letters next to each other.
'pressure' becomes 'p' (abbreviation).
'air' after 'p' is 'pair'.
'des'+'pair'='DESPAIR'
(Other definitions for despair that I've seen before include "gloom" , "Despond" , "Hopeless" , "Misery" , "displaying lack of optimism" .)