The possessive noun peoples’ is correct when you want to talk about something that belongs to more than one cultural or ethnic group.
If you want to talk about something that belongs to one specific cultural or ethnic group, you would use the form people’s.
For example, “the Spanish people’s opinions” refers to the opinions of just the Spanish. But, “the French and Spanish peoples’ opinions” refers to the opinions of both groups.
If you are writing in a legal, official, or technical context, it may be better to use persons’ as the possessive plural. This is because “persons” is preferred to “people” as the plural of “person” in these contexts.
The QuillBot Grammar Checker can show you whether to use persons or people and if you’re using peoples’ and people’s correctly.