Earlier quoted context omitted.
You know these territories regularly vote on independence, right? https://www.rnz.co.nz/international/pacific-news/375335/tahi... And the answer is usually "no", because most of these islands are poor and get net funding and support from France (or whatever other country holds sovereignty).
If you're talking about New Caledonia it's as really biased view. It was a special agreement following a stron crisis with the Kanak independance mouvement that allowed to agree on 3 independance votes. There's a big difference in votes between the people from metropolitan France and a much stronger support for independance in the Kanak population. We'll see next year what's the result is going to be, but the last on…
The past referendum results mean nothing, they were not rejected because people did not want to be free, but because they don't know who they are. And an independence vote won't be like Brexit, France actually agreed to let new Caledonia resident keep their french passport and rights if they chose to go independent, the effective change will by that social services, police, healthcare will be run by New Caledonia people, but it won't change private rights until next generation. Its a hard question anyway.
I've stayed a year in French polynesia small islands (and ocean, mostly ocean...), i'm pretty sure the only islands that want to leave are the ones with the international airports (and i'm not sure about Bora Bora, never went there). Those with offshore ressources especially don't seem to trust the independence party for whatever reason (it might have changed since then).