Firstly, I'd agree with Iguanamon that France and Belgium are still huge. I find it weird that so many americans go to Europe and want to see it all in a week and spend more time in buses and airplanes than actually in the places on their long list.
I am not telling you to visit just one city, no. But I find it a good plan to choose a region. You'll still have plenty to see and experience (it is actually hard to find a place in France with nothing interesting to see. But I found one! Perhaps you could say it was interesting how uninteresting and ugly that one town was). The choice of region affects the costs a lot. Paris is the most expensive sure, but I doubt you would like to miss it completely. But each of the regions is fascinating and different. Depending on how long you can stay, you can choose the region or two or several.
I personally love to travel by car with several stops on the way somewhere. My family and I explored three or four towns on my way to Bordeaux and back, and on my way from Oviedo. That gives you the most freedom and opportunity to find something unexpected. But there is no reason not to travel like that by public transport at all! When I don't need to carry tons of luggage (and tons of books), I'll definitely try it out. A chain of several interesting places.Or the other option is staying in one place and exploring the surrounding areas by public transport (I have experience with French and Spanish buses between towns and with the railways in both countries and there is nothing to worry about in either of those). Or a combination.
There has been a lot of good advice on cutting down the housing costs. I would recommend airbnb, I have good experience with it. You can find great offers for good prices, especially if you don't mind staying further from the city center. Or just behind the city borders but still on the bus/tram lines. It pays off to do your research and think whether it wouldn't be interesting and authentic to take a twenty minute ride to the city and pay ten euro less per night.
Also, airbnb gives you more often the option to cook your own meals (some hostels do as well, at least in a limited manner). Cooking is definitely a great way to cut down the costs. Sure, try out the local restaurants sometimes, but it is definitely not necessary to eat out all the time. The prices in the supermarkets are reasonable. I think that you, as an american, might even find it much more affordable than what you are used to. All my friends going to the US were rather shocked by the prices of good quality food. The price/quality ratio is awesome in France. Very good basic stuff is just as expensive or sometimes even cheaper than in the much poorer Czech Republic.
About the public transport: look up the prices of ticket for an individual ride and for a day. I guess you won't be staying for a month anywhere, but one week tickets sometimes exist for tourists, as a part of a package with sales to the museums for example. Sometimes it is not a too good offer, sometimes it is great. As was said, buses are often the cheapest. The trains are rather expensive in France (but I think they are more expensive than the buses everywhere in Europe). If you book your ride in advance, you can often find a better price. Some times and lines are simply more popular than others.
Sure, awesome and hyper famous stuff like Louvre simply has a price. But there are often beautiful monuments, castles, museums, zoos, and wonders of nature, which are less known and still awesome. Lower prices, fewer people, awesome. There are even completely underappreciated towns! For example Metz (Lorraine)! A beautiful town with one of the most beautiful cathedrals I've ever seen with windows by Chagall! And also several interesting modern buildings, one of which is a small but great museum of modern art, Centre Pompidou-Metz. I was there twice and there were always several exhibitions with at least one really touching my heart. There is also renaissance and various other styles. The atmosphere of this smaller town is just precious, just walking through it and exploring is enriching, and the density of tourists is really low for France
Really, there are tons of awesome experiences that don't cost an arm and leg, and also include fewer tourists, which is nice. Thanks to your knowledge of French, you can plan your travels much better than a usual tourist, as there are tons of resources on the internet about each region or town.