In the Middle Ages “peoples” was not an uncommon word, but later writers grew wary of it because “people” has a collective, plural meaning which seemed to make “peoples” superfluous. It lived on in the sense of “nations” (“the peoples of the world”) and from this social scientists (anthropologists in particular) derived the extended meaning “ethnic groups” (“the peoples of the upper Amazon Basin”). However, in ordinary usage “people” is usually understood to be plural, so much so that in the bad old days when dialect humor was popular having a speaker refer to “you peoples” indicated illiteracy. If you are not referring to national or ethnic groups, it is better to avoid “peoples” and use “people.”
The possessive form “people’s” is of course fine in sentences like “If elected, I will do the people’s will.”