Part of bedding of the French surgeon (5)
I believe the answer is:
duvet
'part of bedding' is the definition.
(I know that bedding has part or parts duvet)
'of the french surgeon' is the wordplay.
'of the french' becomes 'du' ('of the' in French).
'surgeon' becomes 'vet' (veterinary surgeon).
'du'+'vet'='DUVET'
(Other definitions for duvet that I've seen before include "Type of quilt" , "Bed quilt" , "Eiderdown" , "Bed-cover" , "Continental quilt" .)