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. This happened no just because of the borrowings between cultures, but because centuries ago these nations speak one single common language that has diverge in centuries into different dialects.
More over it is more or less researched how the words and the grammar rules have evolved from the proto-language up to it's modern form. So in fact we can (again, at some extent) translate many modern words to their ancient form, and then translate them back into another modern European language. Of course it is not always that simple process, and there is a lot of exceptions and difficulties, and the true borrowings too. But I think that understanding just some common ideas of linguistics could help in studying of foreign languages (from the same family of languages). At least maybe it will be more fascinating than just a pure memoization.
[1] https://en.m.wikipedia.org/wiki/Proto-Indo-European_language