AEM Cloud - url in page properties is not converted from en to fr in language copy

What synchronization actions do you have configured in the livecopy? Checking https://experienceleague.adobe.com/docs/experience-manager-64/administering/introduction/msm-sync.html?lang=en (which applies to newer version as well), you probably want to include the "referencesUpdate" option as well.

To change the path of an author content fragment in a language copy to include the language code (e.g. "fr" for French), you can use the "Rewrite URL" feature in Adobe Experience Manager (AEM). Here are the steps you can follow:

1. Navigate to the "Rewrite URL" page in AEM. This can be found under "Tools" in the global navigation menu.

2. Click the "Add Rule" button to create a new rewrite rule.

3. In the "From" field, enter the original path of the author content fragment (e.g. "/content/dam/content-fragments/authors/en/some-name").

4. In the "To" field, enter the new path that you want the language copy to have (e.g. "/content/dam/content-fragments/authors/fr/some-name").

5. In the "Language" field, select the language that you want this rule to apply to (e.g. French).

6. Click the "Save" button to save your rewrite rule.

With this rewrite rule in place, any language copies of the author content fragment with the original path will be rewritten to the new path with the language code included. You can create additional rewrite rules for other languages as needed.

It is important to note that the rewrite rules you create will apply to all content in your AEM instance, not just author content fragments, so you should be careful to ensure that your rules do not conflict with other content paths.