Girl -- Frenchman going after one (5)
I believe the answer is:
irene
'girl' is the definition.
(I've seen this before)
'frenchman going after one' is the wordplay.
'frenchman' becomes 'rene'.
'going after' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'rene' after 'i' is 'IRENE'.
(Other definitions for irene that I've seen before include "- - Handl, actress" , "Peaceful girl" , "Goddess of peace - Byzantine ruler" , "- - Worth, actress" , "US actress, -- Dunne" .)