Remains of the French Saint (4)
I believe the answer is:
dust
'remains' is the definition.
(dust can mean a person's remains)
'of the french saint' is the wordplay.
'of the french' becomes 'du' ('of the' in French).
'saint' becomes 'st' (abbreviation).
'du'+'st'='DUST'
(Other definitions for dust that I've seen before include "Powdered eart" , "Hopes to turn to this" , "Powdery dirt in dry areas" , "Powdery matter" , "Do some housework - we all come to it!" .)