The difficulty I see for this Kindom forming is that the Indians living in Patagonia weren't living under any sort of entity that encompassed them all, so, even if some factions chose Oriele-Antoine as King and support him, others probably won't.
Structures and alliances changed a lot. Around 1870, in what would become Argentine Patagonia, the main "entity" was the confederacy led by
Calfucura which extended from the Andes to the center of the modern province of Buenos Aires, across the Pampas. But, North of it, tribes like the ranqueles, in (modern) southern Cordoba, didn't answer to him. And, to the Southwest, in the more densly populated Neuquen, Lonko Saihueque didn-t answer to him, and was instead an ally of the Argentine government. At the same time, the few Tehuelche Indians living from the South of Rio Negro to the Maguellan Strait answered to Saihueque, not to Calfucura's Confederacy. And I guess in Chile, where Indian population was higher, divisions would be more profound, and there'd probably be more entities than on the "Argentine" side of the Andes.
Also, it's not that the Lonkos were Kings that could order anything or crown whoever they wanted. The system was a mix of a sort of feudalism with tribal protodemocracy. On the one hand, the Lonkos were the supreme commanders at war, and could "call the banners" before attacking, but nothing granted that smaller "capitanejos" would come with their men. On the other hand, important decissions like signing peace with Huincas (Christians) or going on a raid were talking after long talks that might last for days, called Parlamentos, where anybody could speak and speakers couldn't be interrupted.
These aren't unavoidable obstacles, but you need to have all (or at least most) of Patagonian Indian groups feel very threatened by Chile and Argentina (which isn't extremely hard, you just need them all to see what devastating effect Remington rifles would have on them) AND to have them ALL believe that crowning this French guy is the only solution for mantaining a sort of independence and preserving their way of life. The second is the hardest part. It might helped if he had been supported by his motherland, and came with a few soldiers and lots of rifles to give in (if, instead, he comes with lots of soldiers, they might see HIM as a greater threat than Chile and Argentina, instead).