The hopelessness of French resort one runs (7)
I believe the answer is:
despair
'the hopelessness' is the definition.
(despair is a kind of hopelessness)
'of french resort one runs' is the wordplay.
'of french' becomes 'de'.
'resort' becomes 'spa' (spa is a kind of resort).
'one' becomes 'i' (Roman numeral).
'runs' becomes 'r' (cricket abbreviation).
'de'+'spa'+'i'+'r'='DESPAIR'
(Other definitions for despair that I've seen before include "An unhappy state" , "Give up hope" , "sort of counsel?" , "Complete absence of hope" , "The feeling that nothing will turn out well" .)