Mediterranean island the French cry about (6)
I believe the answer is:
lesbos
'mediterranean island' is the definition.
'the french cry about' is the wordplay.
'the french' becomes 'les' (les is the in french).
'cry' becomes 'sob' (sobbing is a kind of crying).
'about' says the letters should be written backwards.
'sob' back-to-front is 'bos'.
'les'+'bos'='LESBOS'
(Other definitions for lesbos that I've seen before include "Jot" , "Island, home of Sappho" , "Greek island -- home of 3" , "Greek island, birthplace of Sappho" .)