Me and my missus did this after leaving uni. We had siz weeks, during which time we went from Paris (to see the tour), to Bruges, Amsterdam, Cologne, took a boat down the Rhine to Frankfurt, then Munich, Neuchwanstein (Fairytale castle), Venice, Florence, Rome (Orsumz! But l am a history geek), up the coast to Genoa via Pisa and Cinque Terre(scenery!), then finally through Switzerland via the Glacier Express (secenery again!), Freiburg in the Black Forest, Strasbourg, Paris, home.
You could do all this in a month as we spent the best part of 4-5 days each in Paris, Rome and Genoa. My tip would be to take small, packable items eg travel towel, anti bac gel etc. Comfy, BREATHABLE shoes (you will walk, a lot). Get hold of the european train timetable and a couple of phrase books. And something to read - trains can get a bit dull after a while.
Best. Trip. Ever.