Mathieu,
Can you test on our Canvas app and see if you run into the same problems:
apps.facebook.com/joomla-extensions/
We just did, and we were logged in just fine with Safari v5.1.5. Knowing if you have the same problem there (or not) will help narrow things down. Either way, can you post (or Private message) your Canvas URL to us so we can test there as well?
Thanks,
Alex