PLEASE can someone explain CAF to me?

You do need a French bank account for the CAF to be paid into. You need a lot of paperwork, they will give you a list of the things you need when you go to see them. There's usually a building in the city dedicated to the CAF which you need to go into and speak with someone. The application system is very long and very complicated - I know there is a stereotype about French administration but the CAF really is horrible. You will be called back numerous times to give them yet more paperwork, and copies of what they have lost.

Unfortunately it is very likely that you won't receive the CAF. I applied for it in October and I still haven't received it, I've given up all hope now. Many other people I knew were told that they weren't eligible for various reasons. They are very, very reluctant to give it to foreigners. That being said, it is definitely worth applying as it can cover a significant portion of your rent. Just don't rely on it.

Here's a handy article about the CAF too! :)