Mathieu,
We actually just got some time to look into this, and wanted to wrap our head around the problem since we're coming out with 4.0.2 this weekend (minor bug-fix release). While the above suggestion obviously works, we'll be implementing a different change in 4.0.2 to allow user's to login through the JFBCLogin form, but actually processed by CB.
The change is at the top of the same /tmpl/default.php file. At line around line 20, you'll see:
$passwordName = 'password';
For CB, this should be:
$passwordName = 'passwd';
In Joomla 1.5 and CB in general, that's the name of the password input field. In Joomla 1.6+, it was changed to 'password', which is why the user wasn't getting logged in.. it looked like they didn't supply a password.
Feel free to make that update, or leave it how it is. The end result should be the same either way, and in 4.0.2, you won't have to worry about this.
Alex