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The French sold the territory to the US because they were fucked up from their own wars and had no actual capacity to settle, control, or extract value from it. It was a way to get money out of an already existent reality. If the French instead held onto it out of stubbornness, they do worse in their European wars without all that American capital. Assuming the US state respects the settlement boundaries (which they would probably sort of do, as they didn't go invading Canada in this time), you'd have smaller than historical waves of American settlers entering into legally French but de facto Native territory. They wouldn't have as much support from the US state. The US would not be as effective at expelling the Natives in the east without someplace to force them to, and they could either be more violently genocidal or be forced to recognize more indigenous rights and autonomy.

Taking the more optimistic view, the smaller waves of western settlement lead to greater degrees of integration and cooperation among Euro settlers and Natives, as was often the case in the first phases of settlement in a given area before it ramped up with state legal and material support. Native nations west of the Mississippi would be better able to secure economic leverage against the US, which would remain constrained to the eastern ~22 states. Native nations would end up close to fully exteripated in the mid-Atlantic, as they are today, but probably much more prevalent in the South, upper New England, and the 'West' (west of the Ohio, essentially). The US still becomes a major industrial and agricultural power, but its explosive growth is restrained without an endless frontier, and class conflict would be much more intense as a result. That will probably end producing a far more left-wing country by the end of the century, and one far less capable of breaking out of its continental barriers and establishing its global empire.

We don't really know a lot about what large-scale, long-term French settler colonialism would look like in the Americas. Spanish and English settler colonialism were materially different in many important ways leading to wildly different outcomes for the indigenous nations, but the French were out of the game with the Lousiana Purchase and the loss of Haiti. My guess is they would take an approach of extensive trade, where settlement is focused on major waterways and largely commercial rather than agricultural. France would not bother with the important of large numbers of African slaves into the territory and would not carry out comprehensive genocidal efforts against indigenous nations. Instead they'd maintain large scale fur trade and probably want to arm Native people to prevent the US from taking over in systemic fashion. You might end up with a colonial capitalist elite from a wide variety of European, African, and Native backgrounds who speak a creolized French that becomes a lingua franca among settlers and Natives. Many Native nations have a smoother entry into the capitalist world system while retaining most of their traditional lifeways and languages. The territory inevitably becomes formally independent sometime after Mexico. If the patchwork factions can pull together a pseudo-state confederation for mutual defense and international representation, they'll be able to roughly stabilize themselves from fuckery from the US and Europe. It acts as an essential commercial power linking the US and Mexico and providing access to the most ecologically rich part of the continent.

The native nations of Washington and Oregon may be able to successfuly play Canada, Franco-America, and Mexico against each other to retain economic and political sovereignty - they had a well-established and highly developed class society that could have transitioned into capitalism if given respite from the US's incomparably genocidal violence. Russia retains Alaska and no major settlement moves are ever made there. Under the USSR it becomes the most autonomous and least-developed zone in the Union except for a single port city.

Mexico retains its land and ultimately emerges as a large and powerful capitalist state with a world-dominating oil industry, the world's longest coastline extending from Chiapas to the redwood forests of California, and a much stronger campesino political class without US fuckery.

We end up with a North America split along three major European-derived axes each with very distinct sets of Native nations and multinationalism. They roughly balance each other to the benefit of Natives and workers, and the class conflict intensification within the US propels it into socialist revolution shortly after the USSR. In the middle and west of the continent, Native nations largely retain territorial integrity and don't suffer anywhere near the same levels of dispossession and violence, though they definitely still end up marginalized in many more populated areas in ways that look more like modern Mexico than the modern US.