Any reason why they didn't get their own "meat name" then? I thought that the "cow/beef"-"pig/pork" split was due do that, with the initially Norman nobles consuming most of that luxury meat. Thus nothing for "chicken", either. Did "lapin" or something like that get lost?
We did get poultry from French poulet
The introduction of rabbits to England post-dates the Norman conquest.
Yes, cony: https://en.wiktionary.org/wiki/cony#English
See also the note at rabbit: https://en.wiktionary.org/wiki/rabbit#English apparently rabbits themselves are all French. "hare is indeed inherited from Proto-Germanic."