Do French territories hold French passports?

Question

Do people in French territories (i.e French Polynesia or Vanuatu) hold French passports, and do they have the same priviliges as the mainland French (i.e visa-free travel and residing in any EU state)?

Answer 1

Yes.

Answer 2

My understanding is that the Overseas Departments and Territories are fully a part of the  French Republic and that their nationals are entitled to full French citizenship.