Yes, Steve.
"Peoples" collectively refers to a number of races or nationalities (multiples of the American people, the Japanese people, African-American people, Chinese people, &/or Asian people etc).
So if you want to refer to several races you could say
"Western Peoples", referring to perhaps the Europeans and Americans.
In the case of your previous post, the Japanese were accused of copying products from the Americans, British, French, Italians and Australians.
(To name just a few! These days the Chinese are accused of the same crime.)
I therefore considered that you were referring to several
peoples, which made your positioning of the apostrophe correct.
The singular "people" is the collective noun for persons. If you wish to use it in the possessive, it is "people's"

as in, "The people's wish for law reform will be implemented."
(Referring to all the people who voted at an election.)
Compare that with the
(very PC) statement, "The wishes of the First Peoples
(Aborigines, as there are many tribes/families of them) will be implemented." which would be otherwise expressed as "The First Peoples' wishes will be implemented."
See? Simple, isn't it!
(Should I complicate things by discussing "
Aborigines' " and "
Aborigine's"??? Nah. Another day...

)
Normal transmission will now be resumed...