I would suggest flying into Zurich. You could spend a day in Zurich if that interest you and also it would be nice to rest up. I suggest taking the train to the Lauterbrunnen Valley. It is about 1 1/2 hours from Zurich with about 3 connections (via Bern, Spiez and Interlaken). It will offer some of the greatest alpine views imaginable. You can take a gondola up to a tiny alpine village called Gimmelwald. The hikes are filled incredible with views of the Eiger, Monch, and Jungfrau Mountains.
After a couple days of hiking, you can take the train to Lake Como, which is a beautiful ride (Milan is just ok so you can skip it). The ride is only a couple of hours as I recall. Lake Como also offers great hikes. You can take ferries to different towns on the lake. Bellagio, the most famous town on the lake, is a little ritzy for my taste. I stayed in Menaggio which has great trails into the mountains. Varenna is also great.
After Lake Como, I suggest taking the train to Verona. It is a beautiful medieval northern Italian city. It is not too touristy. You could spend 1 to 2 days in Verona. Verona is only about an hour from Venice. Even though Venice is engulfed with tourists, I still think it is worth spending a couple days there. If you walk the back streets, away from St. Mark's square, you will see the real Venice and it is breathtaking.
After Venice, you could go north to the Dolomites. I have never been but I hear it is incredible. You could also go south to Florence and Siena which are incredible, yet obviously a little stressful with tourists.
If you go the Florence route, you could take a train to Cinque Terre after and spend a few days there. 5 amazing towns on the sea. From there you could take the train to Nice via Genoa.
If you decide not to do Florence or stay in northeast Italy, I would suggest flying from Venice to Nice on a low cost airline like Easy Jet. I have never been to south France so I cannot give any advice there.
You can fly home from Nice or Marseille, probably via Frankfurt. No need to make it a roundtrip from Zurich. This is how I would do it but obviously there are many different ways you can plan your trip. Hope this helps!