From what I can work out, yep it seems that way. Pork and beef were too expensive for the peasants so they just referred to them as the animals they were raising, but chickens were actually on their menu so we ended up keeping the animal words for it. We still got the word for pullet (young hen) though.
I just read a theory that poisson, french for fish, didn’t come over because it sounded too much like poison, but who knows if that’s true lol.