For example, in English the word right (opposite of left) and right (privileges, as in human rights) are homonyms. In Spanish, derecho/a also means both of those things. Don’t the concepts behind those words predate the cross-pollination of the two languages? Why do they share this homonym quality?
I think the short answer is that we all speak “Latin” and the various empires, especially Roman, spread cultural concepts across Europe that would be durable for some degree for centuries.
Counterpoint, there are also plenty of false cognates between any given European languages.
There is also convergence, as another commentor pointed out. If something is invented in the US in 1970, or introduced to the US in 1970, there’s a good chance people aren’t going to give it a name in their language: they will just call it what it was called to them.
I don’t think “loan words” explain your example, but you can imagine that if what is now Spain and France had the same rulers, they’d develop similar legal culture later on, and then if France conquered what is now England, that eventually English would inehrit specific quirks common to Spanish