I don't know that the Native Americans had the same concept of expansionism that the Europeans had. They also lived under a different set of circumstances than the Europeans which affected their cultures and ways of thinking and living (see this thread where we discussed some examples).However - since this is a "What if?" thread - I'm going to have to say that they would have sought sparsely populated areas at which to set up trading posts. In America, tribes didn't seem to congregate in large "urban" areas, so in Europe they would be more likely to encamp near creeks or rivers with nearby woodlands and good hunting opportunities. Seems like those kinds of places would have been plentiful in Europe during the late Renaissance period, so avoiding large cities (London, Paris, Lisbon, etc.) would have been the plan.
But would the cities have been so large or intimidating to the Indians had Europe not had the technology? But since were playing what if, here goes: Some tribes did have the expasionistic tendencies, they just didn't have the means to go all out with it like the Europeons. Like the Sioux did when they left Minnesota, or even the Iroquois. In my mind men are all generally the same when it comes to the basics, if the tables had been turned then Europe may have experienced similar histroy as we did here in America. The Indians were warring, stealing land and enslaving one another long before Europe came in to the picture. No ones innocent.
i am not sure they would succeed. the population of europe was a lot larger to the native americans. weapons are one thing but huge numbers is another.i would think they would invade somewhere closer to home to europe.
If Europe had been no more advanced then the North American Indian, The Indian would have won that war. The Sioux, Apache and Comanche were among the best Guerrilla fighters in the world, the Europeans could not have matched that in the end. But then again what period of European history are we talking about? I think the further back you go the better chance they would have had, as their life was more primitive, more in line with the way the Indians were living.