I am not sure that holds because the same split is observed in other languages, too. See el pez vs pescado in Spanish, for example.
Does the same (different source languages) is true for “el pez” and “pescado”?
"The English peasants raised the sheep, the French masters eat the mouton." <-- this is the non sequitur
My comment was about French as such (being spoken in France by French masters and their French peasants).
So then in the case of English, the different meat names came about in a different way, from two languages that separately didn't have two meat names, which is interesting.