Travel from Paris to Nice

Hi! I am an American college student who will be spending ten days in France next month. I will be traveling with five others. We are very much on a budget and trying to keep spending as little as possible.

We have a flight into Paris, then we will fly out of Nice ten days later. We have found housing, but are currently searching for transportation. Our main question: what is the most affordable way to travel from Paris to Nice? And, if anyone has any advice on how to find cheap transportation around the cities, that would be helpful. If anyone has any general tips for staying low-cost, please share! Thank you.