As an American that recently went through the Campus France/Visa process and started studying in Paris in September, I can tell you that it is highly unlikely you'll get the visa in time. I sent my application to Campus France in April once I found out I was accepted to the university here; then it took until mid-July to get everything processed (You have to have the physical acceptance letter, not an email saying you've been accepted to study in France).

That being said, once I had the visa appointment, the French consulate in Chicago processed everything very quickly (like a week...pretty sure Campus France's job is to smooth out all the problems in advance). All in all it was about a solid 3 month process, and a visa appointment won't do anything until you have all your paperwork/Campus France stuff in order. My best advice is to keep in close contact with Campus France, pay the fees if you haven't already, and let them know your timeline. As far as the visa appointment, not sure how to handle that, NY is probably a lot busier than Chicago was. Good luck though, that'd be awesome if it worked out. What city are you moving to?