Almost everyone who applies to the Assistant program is accepted. The only real criterion is that you are a native speaker of your language. This is not to say that the application process is easy, especially if you are unfamiliar with French paperwork. Don't be discouraged if there are parts of the application you do not understand. Ask your French teacher for help, or ask on the discussion page.
Note for those applying from the United Kingdom: The easiest route is via the British Council Assistantship Scheme, this requires no french paperwork. It is also worth noting are now entitled to an ERASMUS grant from the EU if you are applying through a UK University (and you are of EU nationality). This grant can be worth a lot of money, so it is well worth finding out more about it.
The American version of the application, which is mostly in French but has some instructions specific to American assistants, is available at the French culture site.
The file is in Microsoft Word format, and it is possible to fill out almost the entire form on your computer. It's best to print the completed application in A4 size paper if you can find it; otherwise it will be shrunk to fit American paper's dimensions.
You will need a passport sized ID photo to attach to the application. Shop around a bit for these (drugstores, photo labs, copy shops…), as their prices are often unreasonable. Look for eight or more for less than $10 — you will need more photos for paperwork before and after you get to France. Remember that French passport pictures are 35mm by 45mm, not the American 2 by 2 inches. It's ok to have an American one for the application, but for later photos, they have to be French sized.
On page 10, the application asks for your “preferred geographical location.” You are allowed to specify three académies in order of preference — these educational divisions correspond with the administrative regions of France. All of them are large, and you will have no opportunity to make your request more precise. Many assistants request the Paris académie — dreaming of a glamorous life in the Marais — but are placed in some scary Paris suburb.
It's best to find an entire region that might be interesting to you. If you like mountains, select a region near the Pyrenees or the Alps. If you are attracted to Italy, Spain, Germany, Belgium, Luxembourg or Switzerland in addition to France, select a region close to the particular border. If travel is important to you, make sure you select a region that is well serviced by the SNCF (the railway).
Another consideration to take into account is the size of town/city you will be placed in. If you're placed in Paris or any other major metropolis you'll have a ready circle of fellow assistants. However, you can also be placed in a tiny village where you're the only language assistant (which can be lonely). There are three checkboxes for specifying the size of town/city on the application, from a rural town to large metropolis.
Here is a link to a well-detailed map of France.
Also, here are links to downloadable maps of the train network and TGV routes.
You also must select what level of school you would like to work in. Different levels of school have different contract lengths. IUFM assistants work for 6 months; high school assistants for 7 months. Primary assistants have two options: a contract of 7 months where they work along side a French teacher, or a contract of 9 months where they are expected to plan the lessons and lead the class by themselves.
High school assistants generally speak much less French with their students and much more of the language they are teaching. If you teach in primary schools, you're likely to spend most of your 12-hour week speaking French (which can be good practice). Some high school assistants receive very little guidance from the teachers. It is not uncommon for a high school assistant to get nothing but a key to a classroom and a schedule of when they need to be there. It all depends on the individual school and the teachers there.
Your first acceptance letter (the lettre de présentation) only tells you which académie and school level you've been placed in, and it can come as late as mid-summer if you have previously been wait-listed (as of the 2011-12 application cycle, most acceptance e-mails seem to have gone out by late May for applicants chosen in the first 'round' of selections). Shortly afterwards, you'll receive an arrêté (administrative order) telling you in exactly which schools you've been placed. The arrêté can arrive as late as mid-August, so if you're still waiting on it as summer goes on, don't panic (yet)! Usually the TAPIF office in Washington, D.C. asks that participants who have not received arrêtés by mid-August contact them, so that they can try to track it down or at least help assistants determine the best course of action to try and get their visas and arrive in France on time. (NB: The most recent Assistant Handbook states that questions regarding the whereabouts of arrêtés will NOT be addressed before mid-August, so as hard as it might be to wait, hold off on e-mailing the program coordinator until that time. Chances are it IS on its way.)
If the first letter mentions “Toulouse,” however, don't start looking for apartments in Toulouse. Each académie is named for the largest city in the region, but only a few of the assistants in each académie will actually be assigned to schools in this 'capital' city. It is therefore best to wait until you get your specific placement to search for housing. Do, however, start looking for plane tickets.