Hello @jeffunik72,
You need add this code <?php do_action('icl_language_selector'); ?>
instead of the one that you’re using now. That code is suggested by WPML to use in php files.
If you still want to use your code you need add a link to French site in the code <li><a href="#">FRANÇAIS</a></li>
instead #
.
Regards,
Eva Kemp.