Bird very lucky to avoid Frenchmen (3)
I believe the answer is:
jay
'bird' is the definition.
(jay is a kind of bird)
'lucky to avoid frenchmen' is the wordplay.
'lucky' becomes 'jammy' (jammy means lucky in a smug way).
'to avoid' is a deletion indicator.
'frenchmen' becomes 'MM' (two M's - M is short for Monsieur).
'jammy' with 'mm' removed is 'JAY'.
'very' is the link.
(Other definitions for jay that I've seen before include "Colourful British bird" , "Colourful type of crow" , "Garden bird" , "-- Gatsby, F. Scott Fitzgerald character" , "Bird of the crow family with blue plumage" .)