Many of the natives tried to build exactly the kind of alliance you're talking about, but practically, such a cause was always doomed: steel tools and gunpowder were simply too powerful as force multipliers to ignore, and weaker tribes saw no practical diffrence in being evicted from their land by a rival tribe instead of the Europeans.

And once a tribe takes to using gunpowder weapons and steel, it's stuck: killing all the Europeans is the same as signing one's own death warrant, because the skills needed to be independent are lost. Even if they accept that, all that changes is that the French take over instead.