It's different with Europe. As you note, there tends to be a lot of fascination and admiration of the culture there. I still remember the sheer amazement on the faces of my cousin's children when they were asking me asking me "Dwayne, bist du indianer?"
But truthfully, the term is both a misnomer and a bit of a slight. Those original explorers who came to the Americas were looking for a route to India and thought they'd found it, so calling the people of the Americas Indians seemed appropriate. Once this was determined to be false, the term indian is now like a shortened version of indigenous. It carries with it a lot of negativity.
Usage is contentious, as official government departments still use it in Canada and the US. Even action groups like AIM (The American Indian Movement) still use it. First Nations, American Indian, Indigenous are all acceptable. It's a little difficult because as a group they are not homogenous but rather consist of many different tribes with their own customs and traits. It would be impossible for outsiders to keep up and we keep changing what we think is acceptable as well.