"The relationship between the peoples of the United States and Canada is excellent."
Translation:La rilato inter la popoloj de Usono kaj Kanado estas bonega.
You're right that persons is barely used, and generally only in techincal jargon. The normal plural of person is people, and you should basically always use it.
But there's also a singular word people, which is the one being used here. It refers to a large group of people with some sort of national or ethnic ties, and is popolo in Esperanto. Since this particular word people is singular, you can add an -s to make it plural, which is why it's peoples in this example.