The one Frenchman with a girl's name (5)
I believe the answer is:
irene
'a girl's name' is the definition.
(I've seen this before)
'the one frenchman' is the wordplay.
'the one' becomes 'I' (Roman numeral).
'frenchman' becomes 'rene' (common French name).
'i'+'rene'='IRENE'
'with' acts as a link.
(Other definitions for irene that I've seen before include "One can find a girl in Ree" , "US actress, -- Dunne" , "Greek goddess of peace (English name)" , "Girl's name; Soames Forsyte's first wife" , "Goddess of peace - Byzantine ruler" .)