Mathieu,
When you talk about your Facebook app, do you mean on the Facebook canvas area, like
apps.faceboo.com/YOUR_APP, or do you mean on your actual website?
JFBConnect has an "Automatic" registration mode that should create the users once they've approved your app. If that's not working, let us know the URL we can test with, and we'll look into it further.
Thanks,
Alex