“Le peuple français” is singular. This is clearly marked by the use of the singular article le.

Don’t assume that English and French would always use the same grammatical structure. They are different languages. Worse, even in English, you are wrong: the word people in this sense would be singular — a people, i.e. a nation or other community, as opposed to the plural use of people meaning multiple persons. In English, “the French people” is singular.

The sentence “Le peuple français n’est pas un” looks like it’s incomplete — it’s waiting for the noun that should follow un. However, it is also possible that this is a complete sentence, using un in a rare adjectival sense. The word un is then an attribut du sujet. As an adjective, un means “existing as a single entity”, “unified”. The sentence “Le peuple français n’est pas un” thus means “there isn’t a single French people”, “the French people is not united”, “there are several different French peoples”.

I find that Gilles answer is enough but I just want to add :

I think the way you are using “peuple” is due to the fact that you’re not native French speaking thus you have different background… and that’s normal. Every language has it’s idiosyncrasy…

Plural or singular? It’s all about “how do you see it”: that’s a matter of abstraction.

“Peuple”, coming from latin “populus”, means “a community of citizens” considered as a whole and thus as a singular entity…

While “Peuple” is used in singular form and it’s a simple case, many other words in French are ambivalent and can be used to reference “singular” or “plural” while they are in singular form; they are called “noms collectifs”, e.g:

• “foule” -> “Et la foule vient me jeter entre ses bras” (chanson d’Edith Piaf)

• “groupe” -> “Le groupe nominal est déterminé par la nature de son noyau”

• “cohorte” -> “Une cohorte désigne un ensemble d’individus ayant vécu un même évènement au cours d’une même période”

• “ensemble”->”L’ensemble des élèves peut réussir l’examen”

They are all meaning “person+person+person+…+person” while they are used like “person”, thus in singular form…

But :

• “Une foule de fans attendent l’arrivée de la vedette” -> we are insisting on the fact that each one of the fun is waiting, seeing each person apart, and using plural form…

• “Une infinité de personnes pensent que cela est vrai” -> focus is being on persons not infinity, and using plural form…

That depends on the intention of the speaker and where he does put the focus…

Finally, the sentence “La France est une terre de diversité: le peuple français n’est pas « un »” is logically correct and even “compact” as “n’est pas un” (=”not being one”) goes in parallel with “diversité”(=”multiplicity”, “diversity”). Inversely, if France wasn’t a country of multiplicity it would be a monolithical bloc (thus “one” uniform country) without any segregable parts…