The plural of people is peoples and is used when you talk about several groups of humans, usually several ethnic groups: The peoples of Asia are vary varied. It is not used very often, so usually you will use the singular.

The correct phrase is 'people's'. 'Peoples' is rarely used and is typically reserved for referring to distinct ethnic or national groups. This is the possessive form of the plural noun 'people'. Use 'people's' when indicating possession by a group of individuals.