Something didn't upgrade properly. The authenticate call should definitely be defined. You should see it in the /components/com_jfbconnect/libraries/provider/facebook.php file around line 522 is where it's defined.
If there's no authenticate function there, that's the problem. If it is there, some other file that should have been upgraded wasn't.
Can you tell me what version of JFBConnect you were upgrading from? Specifically, were you on 6.0.x before or were you upgrading from 5.x straight to 6.0.3? Either way should work, but knowing which will help narrow down where the problem may be coming from.
Also, are any other logins working (Google, Twitter, LinkedIn)?
Thanks,
Alex