tl;dr- YMMV, every colony was a surprisingly unique experience- even when some of them were right near each other.

I think you are mistaken to exclude New Zealand; Maori were forced in mass off land through violent confrontation and conflict. The mid-nineteenth century Maori wars were so fierce at various points that Aotearoa had more British Marines stationed there than anyway else in the Empire.

The intermarriage that took place early on was usually more between merchants/missionaries who were more interested in converting or establishing commercial relationships with the Maori than the settler colonists who arrived and whom the marines were meant to support and protect. The missionaries and merchants were something of a nuisance to settler colonists since they provided weapons and ammo to the Maori.

As to the French; what happens in North America is unique to that time and place. Racial ideas were less set in stone and recently historical work has illuminated the ways in which just changing your dress could allow you to move between legal and administrative identities which today strike us as racial. So a Frenchmen could adopt local Indian dress and become essentially an Indian- just as an Indian woman could (and did) adopt European dress/religion while passing through or living in settlements and become effectively European as far as the legal codes at the time were concerned. There was a powerful belief that native peoples could become French. By the time of the Revolution (end of the 18th/c) this belief is long gone and few think that Indians (much less the masses of enslaved Africans) can truly become French. There is something of a return to this belief at the end of the 19th/c; which comes through really in French Algeria and Tahiti-- wherein some believe that these other peoples can effectively 'advance' enough to become French. However, by the end of the 19th/c this belief is gone-- there are few people still claiming indigenous populations can be assimilated into a French identity. One of the reasons for this change in policy- from being at least ok with assimilating governed peoples to seeing it as bad policy- is envy at the British and Dutch methods of governance and the belief that if the French government spent more time 'associating' with local leaders rather than trying to make them French, they could make more money. Even in the places where intermarriage was possible (and it was not legally recognized across much of the French empire- there were quite a few half-french babies left in Indochina with no recourse to their paternal progenitor)- it was not really all that common. Aside from New Caledonia and Algeria, none of the French colonies of the 19th/c had large scale settlement, so there was never more than a transitory commercial/bureaucratic population.

Worth pointing out, that even at the time of assimilationist politics, it was really only in a few-- already highly though of colonies-- that this took place. I mention Tahiti, but on the other side of the Pacific in New Caledonia, there was- and still is- very very little intermarriage. There was large scale land alienation and several armed conflicts fought to push the Kanak peoples into reservations.

You really shouldn't be excluding New Zealand. You might be able to make the claim that Maori were treated better than average for native peoples, but that bar is really, really low.

The Treaty of Waitangi, the legal document and formal agreement between the British Crown and some (but not all!) Maori rangatira (chiefs being the closest translation) promised the signatory parties independence, true. But it was ignored by British authorities within months. It was British violation of the treaty (at least, violation in the eyes of those who rebelled) that caused the outbreak of the land wars. Throughout these wars, many Maori rangatira allied themselves with the Crown, either out of respect for the treaty, a desire to maintain and improve relations with the British, or reasons wholly their own. The actions of allied Maori proved absolutely crucial - it is impossible to say what would have happened without their help, but the fact is that they played a massive role in fighting the rebel rangatira, and in supporting the British troops.

But, despite their allegiance and all their help, these allied Maori were punished for rebellion as well, or at the least they received no reward nor special consideration. From top ranking government officials to colonists who just wanted more land, the Europeans repeatedly abused their power to take Maori land, enforce their laws upon Maori who didn't want them, and impose taxation and controls on trade that had little or nothing to do with them. It got so bad that the Treaty of Waitangi was officially dismissed, to stop it from getting in the way.

And that's just the 19th century. The 20th has many more problems all of its own.

The 'why' is going to vary of course with each and every individual, but generally speaking it was greed. The first major violation of the Treaty of Waitangi was the imposition of tax and controls on trade between Maori and European merchants, because the governor of New Zealand needed money. There are accounts of a high ranking soldier of some kind (the name and rank escapes me) talking to local colonists, who outright tell him that they want the Maori's land, and the soldiers are going to take it for them. Notably, the Maori concept of ownership isn't really compatible with the British concept, so land and resources couldn't be so easily gained through things like intermarriage even if the British wanted to try that route.

Most of this information is from "Kupapa: The bitter legacy of Maori alliances with the Crown" by Ron Crosby, with the exception of the soldier's anecdote which came from a collection of his own writings.