Hey Simon,
I would advise you to stay in France for longer than 14th of July. 14th of July is their national day, and they have awesome fireworks all over France at night (around mid-night). If I were you, I would not miss it. The best would be if you could go to french costal towns. The fireworks takes place on the beach and it is very beautiful.
As for staying, there are tons of hotel, cottages, and bed & breakfast (Chambre des hotes) all over France. But remember that France is visited by more than 75 million tourists per year, half of them during summer, so getting a hotel room can be hard. You may want to reserve it in advance. Besides, almost all hotels have special rates during summer so it could be bit expensive for not a very good quality hotel.
As for things to see in France, where do you want me to begin? There are so many things to see in France and that is all over France that it is hard to just pick and point. Since you are in Paris, you want to visit most of the touristic places of course (Tour Effile (visit it at night when it gets dark to see how it shines under lights), The Louvre, Sacré Cour, Notre Dame etc etc). And do not forget to go shopping when in France. Their fashion is way better than the one in USA.
I would advise you to get out of Paris to see the real France; I mean beautiful little villages with stone paved roads with tons of flowers on each side, tons of chateaus, awesome fields, nice beaches etc. If money is not a problem head towards Nice or Cannes (Southern France). Everything there could be expensive though. Or head towards the other part of South of France, towards Pyrenees. It is beautiful there, with high rising mountains and nice beaches. Besides the towns there are beautiful, and you will be right next to Spain. If you like chateaus, go to Loire Valley. There they have tons of them and very old ones.
Honestly, there are so many things to see in France that it is really hard to tell you all of them. It is not the most visited country in the world for nothing.
The good part is, you are going to France during summer, so the weather can be good (weather in France is extremely un-predictable; it would rain, be sunny and cloudy at any time).
And since there will be millions of tourists in France around summer, you can imagine that the French people will be a bit anxious, stressed or even rude. So do not be like any other American that is obnoxious, loud, and arrogant. And learn some French words or phrases; French people love it when they see that you are making some efforts to speak their language when you are in their country.
And the train service in France is very good, so you may not have much problem getting to Spain or Portugal or other European countries.
As for the visa, if you are an American citizen, you do not need visa to go to France and once in France, due to EU, travelling to another country is like going to another state in USA. No problem at all.
Good Luck!
