I traveled with Globus last year to those same places in Sept. If you really want to wear sneakers the dark colored ones are very popular in Europe.The ones that everyone wears look almost like bowling shoes. They are not the clunky ones that people wear here.Seems white sneakers are really an American thing. Everybody in Germany,Italy and France and Switzerland wore sandals.The women wore capri pants or nice slacks,some jeans,NO SHORTS!!!! We traveled the second week in Sept and it was very warm everwhere but London and in the Alps in the early morning. I agree.no t shirts. People do wear jeans but dress them up a little with a nice top. You probably will want to dress up a little for the final dinner. Something like Dockers for men are fine.I never saw anybody in a suit but some of the men did wear a a summer sports coat to dress up for dinner.. . Others just wore jeans and a nice shirt.. . Anything goes with such a diversified group.
Everybody will know your American anyway as you travel around with the tour. Just don't be loud.

no offense intended!!! That is the idea that Europeans have about Americans and it is really embarrasing if someone in the group is really loud! Makes you want to hide under a rock!!!!
Have a great time!!!