Interesting. I've downloaded the French version (I did not choose the Swiss install when prompted in the beginning), and I was able to load the French default template (Modèle AC22 DEFAUT.tpl) and the library (Bibliothèque ARCHICAD 22) into the INT version.
I'm not on Windows, though. I will upload the library here, maybe it is working for you, as your installed one could be corrupted according to your screenshot (it will take some time to upload):
https://www.dropbox.com/sh/f5at41vraqtgd8d/AACxlzWJEo2B_dgsvZMWvJXKa?dl=0
As I've said, I'm using HUN templates/libraries with the INT install with no problems, and the CHE template/library is also working (the CHE version would require a separate key), I don't have experience apart these three (INT, HUN, CHE). It would make no sense to me to put restrictions on the files themselves, that would just make international working impossible (or extremely difficult at least). The localisations of ARCHICAD itself are another issue, there could be some specific developments, etc., the linked video previously demonstrates that, I cannot find that feature in my INT version (?).
The AC22 FRA install is the default 3006 build on my computer – if you have a later one, and the library loading problem is related, I won't know that. I suspect that a repair could solve it, but first you could try downloading mine from Dropbox – I hope it's not against GS rules though...
Edit: I'm syncing other stuff as well, Dropbox says 40min until complete...
odv.hu | actively using: AC25-27 INT | Rhino6-8 | macOS @ apple silicon / win10 x64