The singer with the French name (5)
I believe the answer is:
title
'name' is the definition.
(I've seen this before)
'the singer with the french' is the wordplay.
'the singer' becomes 'tit' (type of songbird).
'with' says to put letters next to each other.
'the french' becomes 'le'.
'tit'+'le'='TITLE'
(Other definitions for title that I've seen before include "Designation of honour, rank or office" , "Name - sign of rank" , "Mr or Mrs, say" , "Caption; name" , "headline?" .)