I, a Frenchman, get the girl (5)
I believe the answer is:
irene
'the girl' is the definition.
(I've seen this before)
'i a frenchman' is the wordplay.
'a frenchman' becomes 'rene'.
'i'+'rene'='IRENE'
'get' is the link.
(Other definitions for irene that I've seen before include "- - Worth, actress" , "Girl's name; Soames Forsyte's first wife" , "Greek goddess of peace (English name)" , "- - Handl, actress" , "Girl's name (meaning Peace)" .)