Looks like that is the case: https://en.wiktionary.org/wiki/Appendix:Proto-Germanic/fulk%C4%85
couldn't "folket" be the people like "the Danish people" and then it would be eats?
If so, it could be either eat or eats, depending on your English dialect, as "the people" would be a collective noun.
Many dialects (including most British English) treat collective nouns as plural objects in this context, so eat is the correct word to use.
Other dialects (including most American English)
get it wrong ; - ) treat collective nouns as singular objects, so in these dialects it would be correct to use eats.
Wikipedia has an explanation https://en.m.wikipedia.org/wiki/Collective_noun#Agreement_in_different_forms_of_English.
As an American, I would never say 'the people eats'. The people eat. It would probably depend on the context of the word we're talking about. The group eats. The members of the group eat.
I've been told by a Dane that "folk" isn't use to refer to a group of people; it's used to refer to a population or something like that. "mennesker" is used to refer to people.
Sometimes you eat the bear and sometimes the bear eats you. That's Life.
Bears are sacred to my people and if you eat bear meat it means you're a medicine man
for me, at this point so far, "de Dansk DL bjørne" are more human and more intellingent than some "folk" I know, so this is cannibalism!!!!