Greek character of the French island (6)
I believe the answer is:
rhodes
'island' is the definition.
(Greek island)
'greek character of the french' is the wordplay.
'greek character' becomes 'rho' (letter from the Greek alphabet).
'of the french' becomes 'des' ('of the' in French).
'rho'+'des'='RHODES'
(Other definitions for rhodes that I've seen before include "Dock for undersea craft" , "Greek island, ten miles off the Turkish coast" , "Island, explorer" , "Shored (anag) - Greek island" , "Horsed around on the Greek island" .)