Some of the Ottawa and other tribes around the Great Lakes rebelled (others hedged their bets and remained neutral; the Ottawa settlement around Michilimackinac, for example, made a hefty profit acting as a middle man between the British and the hostile tribes). Pontiac's War had more to do with Anglo-Native relations once the French had been driven out (and especially the British upending of established gift-exchanges and general treatment of the natives as conquered subjects) than it did with loyalty to the French over the British. While the French had the upper hand in terms of loyalties (supported by a fairly substantial network of marriage ties between French traders and local leaders), there were always plenty of natives who were flirting with supporting the British. The aftermath of the Fort William-Henry Massacre, in particular, had led to most of France's native allies abandoning the cause; they would be less happy with France massively expanding its military presence in the aftermath.The Cherokee stayed hostile until the end of the 18th century OTL. Furthermore the war was started by the settlers and many leaders of the Cherokee had already turned to the French prior to the 7YW.
The Cherokee didn't really have a lot of feuds with the tribes north of the Ohio, that were the Iroquois.
The Ottawa and most other tribes around the Great lakes rebelled against the British after the 7YW so in any case they preferred the French over the British.
As for the Cherokee; while they came into contact with the northern tribes less than the Iroquois did, there were still frequent back-and-forth raids by both sides (this was one of the things that had doomed earlier French attempts at cementing a broader pan-native alliance). Some Cherokee had flirted with the French beforehand (in much the same way as many of the French-aligned tribes of the north had flirted with the British before the war), but the final break didn't happen until fairly late in the war, and only after the British had noticeably gotten the upper hand. While there was definite hostility, the conflict itself had more or less come to an end by the end of the war, and only flared up again during the ARW (when the Cherokee found themselves having to choose between the British and the colonists anyway).
More broadly, it's a mistake to speak of any of the native groups as unified decision-makers; different members of the tribes could and did make different decisions, and they were made on the basis of their own interest, rather than the interests of Paris or London. The same can also be said of the European colonists; after all, it was Virginia, rather than the British Parliament, that made the decision to send out George Washington and provoke the French & Indian War in the first place.
They provide infrastructure, but trade and commerce is still very much dominated by the natives, who may have other opinions on British colonists (generally they were receptive to British traders but skeptical about full-fledged settlements; the same tended to apply to their attitude towards the French as well.France only used its forts for trade because the American push west was pretty much nonexistent prior to the 7YW so there was nothing else to do in the area yet, if suddenly Americans want to enter lands belonging to the French claim then France'd automatically do something (whether it's arming natives or building forts) to act against it or at the very least regulate it or try to use it to their advantage. And you don't seem to have realised it yet, but most of those strategic trading locations were also strategic military locations, especially when routes between those forts become some of the little infrastructure in the area.
As noted, the difference between "Anglo-French Wars" and "Wars with France and Britain on opposite sides" isn't particularly relevant; what matters is that the various alliance webs of the 18th century tended to lead to wars (and if France truly emerges victorious from the 7YW and destroys Prussia, I'd expect at least one of Russia and Austria to form a rapprochement with the British to balance). Once one of these wars breaks out, Britain focusing on the colonies is almost a certainty (if only because it's one of the few places the British can reliably strike at the French), and the Royal Navy means that France will have difficulty resupplying its colonial forces (this was a serious problem for the French in the 7YW OTL), which in turn discourages them from investing too heavily in the colonies, because that's going to be taking away resources from the main theater of operations in Europe (French strategy had always been that any colonial losses could be made good with sufficient success in Europe; the 7YW merely saw them unable to make enough gains in Europe to counter the loss of most of their overseas possessions).There were pretty much no Anglo-French Wars in the 18th century, they only wars they had then were all parts of large European conflicts, namely the Spanish Succession, Austrian Succession, 7YW and American Revolution. Furthermore if the war lasts anywhere as close as it did OTL then Great Britain would still be close to bankruptcy and would still have growing unrest in the 13 colonies so just starting a new war would be asking for trouble. And the British wouldn't be the only ones who learned from the 7YW, the French became well aware that their forts in g.e. the Ohio valley weren't educate for real warfare and that they needed more soldiers in the area (that's why after beating the British back they left Duquesne) so there's a big chance they'd replace the small wooden forts with actual structures (or at least the most important ones, like Duquesne, Presque Isle and Niagara) like when the British build fort Pitt. France doesn't need a local population, they just needed to expand the size of the Compagnies de la Marine and the navy and keep the natives friendly. Furthermore France could almost always count on its ally Spain, while Britain's ally the Netherlands was afraid of a French invasion and Prussian involvement could trigger intervention from Austria, Russia, Sweden, etc.
More broadly, this expanded set of garrisons is going to be extremely expensive, and the French finances were always worse than the British throughout the period. All to protect land that isn't going to be particular profitable to France anyway.