I'll try to explain the situation, if this doesn't work you can get access if you want, just to take a look.
I'll use the following symbology:

• Abcde = Page or Menu
• {xx/yy} = language configured/displayed
• (XX/YY) = template configured/displayed
• └ = click on a submenu or link
• <......> = remarks
• zzz = undesired behavior

<Default language/template: de/DE>
Hauptseite {de/de}(DE/DE) < Main page in german >
└Kameraden {de/de}(DE/DE) < Userlist in german >
└John Smith {--*/de}(--*/DE) <any userprofile chosen>
Page principale {fr/fr}(FR/FR) < Main page in french>
└Camarades {fr/fr}(FR/FR) < Userlist in french >
└John Smith {--*/fr}(--*/DE) <any userprofile chosen, will fallback to the default template, at least thats how I understand what's happening>
*<The profile pages loaded when opening a profile from the userlist are not configured manually, of course, so I don't know how I should create double menu items for them>
<For the bilingual functionnality, of course the following pages are linked: Hauptseite-Page principale, Kameraden-camarades, and also the respective "my profile" pages>

Hoping the best.
Well, hoping that wasn't in vain.

B

Okay, I managed to identify the item ID. The menu item is the "Profiles" entry (Alias: cb-profile).
The template associated was the default.

- I cloned the item to create one for each language (e.g. cb-profile-de and cb-profile-fr)
- I unpublished the default one
- I linked the two language versions
- I associated the respective templates
- Did the same for the cb-profile-edit (etc.)

Works

<can be closed>

B