You mention beef and cow but missed steak and here is where it gets really freaky!

Beef is derived from boeuf. Beefsteak is English. Biftek is French and derived from beefsteak. So the French word is derived from English which was, in turn, French.

A quick search shows that the etymology of steak seems to be Norse. So we have a good old mishmash here. Anyway, the important point is that England invented the beefsteak and exported the concept to France. However they do seem to have accepted the baton and done a pretty good job with it ever since.