Hi Chouby!
I've got the polylang version you have developed a week ago (http://wordpress.org/support/topic/plugin-polylang-custom-type-posts-not-found-with-pretty-permalinks-urls?replies=6)
and with pretty permalinks enabled, the when visiting the home page from a browser with a language different that polylang default, I get redirected to homesite.com/?lang=de instead of homesite.com/de/
All other (header & footer) homepage links are OK - only the language autodetect rediretion.
If you've already correct it - sorry, but I haven't test it yet. Cheers :)