Mathieu,
I recreate what you mention on your site. We'll do some testing, and see if there's something we're doing wrong. With the 4.0 release, we changed the JFBCLogin module to actually use the Community Builder login functionality, which allows user's to login with their username or email address (if CB is configured that way). This was tested a bit with Joomla 1.5, but might have some issues with J1.6/1.7, which you look to be using.
For now, if you're up for making a minor modification to the JFBCLogin module, this will switch it to use the normal Joomla login flow, while still keeping the Register/Forgot password links going to CB. To do so, open up the /modules/mod_jfbclogin/tmpl/default.php file. Around line 55, you'll see:
<?php if ($registerType != "communitybuilder")
Change that to:
Let us know how that goes, and like I said, we'll do some more testing with the newer Joomla versions to see how it goes.
Thanks,
Alex