Looks like that is the case: https://en.wiktionary.org/wiki/Appendix:Proto-Germanic/fulk%C4%85
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.
Yet another ‘wrong’ answer according to Duolingo. As a native English speaker and given that Danish present tenses translate as continuous, if I write “the people are eating the bear” I do not expect it to be marked wrong, presumably by a non-native English speaker. It isn’t and it is annoying to be told that the ‘right’ answer is “the people eat the bear”. It takes all the pleasure out of using Duolingo.