Hi,
happy to help.

Here's how I would do it:

Rule 1: use the Environment tab to set Page URL "Contains" example.org/de
In the Succeed Action (Actions tab), you can use an intelligent redirect that will simply switch the domain but leave the rest of the URL intact. So set "Next Action" to "Redirect", then use the following in the "Redirect URL..." box:

{scheme://}beispiel.org{:port}{path}{?query}{#fragment}

So that uses the same scheme, port (if used), path, query string and fragment from the original URL, just sends it to a different host.

Rule 2: do similar to rule 1. Detect the Page URL containing example.org/fr and set the redirect to:

{scheme://}exemple.org{:port}{path}{?query}{#fragment}

... continue that for as many languages as you have.

Then the next set of rules will set the template for each of the other sites.

Rule 10: in the Environment tab, in the Domain name(s) box, enter:
beispiel.org, www.beispiel.org

(if there are other domains that use the same template, include them in the list with their www version listed too, if necessary)

Then in the Succeed Action, use the "Set TemplateStyle" dropdown to select the template you want to use for that set of domains.

Save the rule and make a new one like that for each of the different domain/template combinations.

Test!

I trust that's all clear enough - but let me know if you need any further assistance.

Best regards
Stephen