Two different URLs pointing to the same Opencart installation?

Hello there!

What I want to do is to have a completely new domain name (for the sake of an example let's call it http://foo.fr) which I want to point to my current store which is under http://bar.de. The reason why I want to do this, is to offer some custom country options for people visiting my store from their "local" domain. Do you have any ideas on how to achieve that?

I already tried using my cPanel's settings but although it displays the page fine, some icons aren't there - I suppose because the URL in config.php is different.

you should add your second domain (foo.fr) in cpanel as a addon domain.
make sure that it is pointing to /public_html, just edit the path in add on domain.

once set up, go into you main shop admin, go to configuration, and add a new shop.