Perhaps, it would be more useful for students if foreign language courses start with explaining one thing that is well known to linguists, but maybe does not have enough recognition by a wide audience. Most European languages are at some extent just dialects of the same common language[1]. And most of the words we use in distinct languages are (at some extent) just different pronunciations of the same vocabulary. Thi…
It's more complicated than that. First, it's more than just 'centuries ago'. Second, there weren't any nations back then. Third, it wasn't necessarily the case that a common language, proto-Indo-European, was spoken over a large area. There was just as much, and even more, diversity of languages back then.
It's just that the speakers of proto-Indo-European brought their language with them when they migrated and/or conquered. Just like the Romans later brought Latin with them and influenced what would later become French and Spanish. The people living 2100 years ago in what is not France did not speak Latin. The people living 600 years ago in what is now South Africa, did not speak Middle Dutch, even though people there now speak a language descendant from Middle Dutch.