The correct plural possessive form is “people’s.” The rule is to take the plural form of the noun and add an “‘s.” “Peoples'” is incorrect as the plural possessive form of “person.” In rare circumstances, you might find it works to refer to a group of people within a community.

People’s is the possessive of the word people — the plural of person. In contrast, peoples’ is the possessive of the word peoples — used to refer to groups of people. Both words are plural nouns, and both are in the possessive form.

While people’s is the possessive of the word people, peoples’ is the possessive of the word peoples – the plural of people. Use people’s when implying ownership of a collective group of humans belonging to a particular nation, community, or ethnicity.