I am planning to move to France and I am a bit curious, how do cellular carriers/networks operate in the European Union? If I have a mobile from Orange, will it stop working once I leave France? Is it like International Roaming here in the US, where you pay through the nose? How does it work?
Using a phone outside of France is easy, usually you need to activate roaming once, for free. If you stay within the EU, it's still international roaming but prices are regulated and going down constantly (there is a plan to forbid roaming fees entirely by 2016 but it's not been voted yet). Placing and receiving voice calls and SMS has become quite cheap, data is still a bit expensive (although you can sometimes buy cheaper data bundles). Obviously, you'll have to decide for yourself if those prices are affordable to you.
Operators in some European countries offer good deals for roaming outside the EU (which is not regulated) but I don't know any in France. Using your French phone/SIM card back in the US could therefore be expensive.
Note that in France, unlike some other European countries, you can get cheap unlimited international calls to many countries on your landline. Nearly everybody I know has a “triple play” (TV + phone + Internet) or “quadruple play” (same plus mobile) subscription that includes this (not your question but I guess it might come in handy).
Within the EU there are (still) roaming fees. However, you might check with your provider whether there are any special deals which can lower these fees (such as for calls from France to another country, as well as for calling France from another country.
It may, however, be worthwhile to get a prepaid SIM card for the other country you visit, maybe together with a simple phone.