How do I find cheap long-term apartment rental in Paris?

I agree with the others. Paris is expensive and you are either going to haver to raise your price or have a long commute. If cost is such an issue for you why not choose a cheaper place to study? Go to Paris on some week ends. You could pick Toulouse, Rouen, Lyons...

Living in Paris is comparable to living in New York... except that if you will be earning and spending in dollars, it will be even more expensive for you. Try to remember that when you are searching for cheap accommodations. You have to go outside Paris to find them (Jersey) and that still isn't cheap. I think you will have to raise your price if you expect to find something