To get the site going again, please edit the /plugins/system/jfbcsystem/jfbcsystem.php file. Around line 26, you should see:
function __construct(& $subject, $config)
{
$factoryFile = JPATH_ROOT . '/components/com_jfbconnect/libraries/factory.php';
Update that to:
function __construct(& $subject, $config)
{
return;
$factoryFile = JPATH_ROOT . '/components/com_jfbconnect/libraries/factory.php';
That should make the site work again.
To get JFBConnect working again, you'll probably need to install the latest version. It sounds like you're using something really, really old. You mentioned an 'update'. What did you update? JFBConnect or Joomla? The latest version of JFBConnect is v7.2.2 and is fully compatible with Joomla 3.8.x. If you're not using that combination, that's likely the problem.
Thanks,
Alex