Songbird the French name (5)
I believe the answer is:
title
'name' is the definition.
(I know this)
'songbird the french' is the wordplay.
'songbird' becomes 'tit' (tit is a type of songbird).
'the french' becomes 'le' ('the' in French).
'tit'+'le'='TITLE'
(Other definitions for title that I've seen before include "inscription" , "Appellation of rank" , "Handle" , "label" , "Name of book, picture or rank" .)