Bruno,
When the user is stored in the database, can you check if their email address is correct/valid? All I can guess is that something is wrong with the email which could be a bug in JFBConnect or a weird response from Facebook.
Beyond that, check if you have any authentication, user or system plugins that may be trying to send an email during registration (or anything else that's different than normal). It's possible another plugin is causing a conflict, but we'd need to narrow it down.
Finally, in the Configuration -> Misc area, turn "Enable Debugging Mode" on and see if any other messages are presenting during registration which may help narrow things down.
Thanks,
Alex