I am travelling to Europe next month, and would like to know the cheapest means and/or modes from Zurich to Nice as I plan to depart from Nice.
The cheapest way is probably ride sharing ("covoiturage") or hitchhiking. But these options require some luck and flexibility.
If you want something more predictable, take the plane or the train.
For the flights, use an engine like Kayak or Matrix Airfare Search to check the possibilities. For the beginning of September I have found one-way flights for +- 110 EUR (Germanwings, Air Berlin, Iberia).
For the trains, you can use Voyages SNCF. I have e.g. found a ticket for 126 EUR by night train via Paris. This has the advantage that you save one accommodation. The price includes the ride plus the bed. On a daytime train you will have to foresee more or less the same budget.
You can also opt for multimodal transport. Easyjet flies from Nice into Basel and Geneva, from where you can easily proceed by train to Zürich. From Basel it is one hour and costs 32 CHF. From Geneva, it is a bit less than 3 hours and will cost 84 CHF. The price for the flight depends on the exact date of travel and the extras you want to take.