I am not a university student but I would like to go to France and take French Language courses. What is the best way to do this?

France-Langue is a program with schools in Paris and Nice. They accept applicants of all ages from high school to retirees, and all abilities from minimal vocabulary to fluent. The best part of the program is that they place you with host families, so it is a true language immersion. http://www.france-langue.fr/en/

If you like an academic-like experience with a strong dose of French culture, I would say the Cours de la Civilisation Française de la Sorbonne (http://www.ccfs-sorbonne.fr/) offers a very immersive program with a very dedicated / experienced faculty.  You can get a 6-month visa through this very well-established program.  You'll hang around at the Sorbonne and meet people from all over.

I really enjoyed Alliance Francaise.  But if you really want to learn, try to live in an environment where you will be forced to speak French to get by.   Nothing pushes you to practice more than needing to speak a language to eat.  My best French progress was when I lived with a family friend who doesn't speak much English, and going to markets where I had to talk to people to buy food.  Wonderful as Paris is, you might want to consider somewhere less cosmopolitan to try to get away from the almost-universal English abilities in Paris.

My advice: buy and study Compréhension Orale level 1, 2, then 3, etc, and use the audio at the same time. Use a dictionary (Google Translate) whenever necessary. After every chapter or two, don't forget to get out and listen to the French / or / try to speak to them in their language. Don't be hard on yourself from the results you get, every small step is a start. About 20 minutes to half an hour being alert is enough. When you're done with the Compréhension Orale series, then buy and study Expression Orale level 1, 2, then 3, etc, and use the audio at the same time. Again use a dictionary (Google Translate) whenever necessary. Try to get and speak more then you did with the earlier books. This way, you'll learn much more than at a language school :) Note: 1. Google Translate, it can translate not only words, but entire phrases 2. Transferring the audio CDs to a MP3 player via a PC will be more convenient 3. Using Google Translate on a tablet is easier than on your smartphone

Cactus Languages runs some programs in France and the Francophonie (countries where French is a predominant language) http://www.cactuslanguage.com/en/home/en-us.php