My father in law is a Persian speaker. I was very surprised to learn that thank you (mersi) is the same as in French, and OK/indeed (baleh) is the same as in Spanish.
Spanish vale and English value have the same Latin origin. Persian bale is an Arabic loanword.
Arigato in Japanese is said to be a borrowing from Portuguese Obrigado (might want to verify that!).
Persian mersi is actually a direct borrowing from the French [1]. Not sure about the other one, but I guess it’s just a coincidence, as happens so often in language [2].
[1] https://en.wiktionary.org/wiki/%D9%85%D8%B1%D8%B3%DB%8C#Pers...
[2] https://zompist.com/chance.htm