For some reason, in the French language itself the same distinction eventually appeared.

In regular language, you would call porc the meat that comes from a cochon, and bœuf the meat of a vache.

It's not as clear cut as in English, as a bœuf is also an ox, and you can also call a pig a porc, but I think it indicates that the linguistic distinction between an animal and its meat is indeed at its core a dehumanizing process, it might just have been helped by the French-speaking rulers of England, but it still happened in France eventually, more recently and without exterior intervention.