session.save_path with no value is normally not a good thing, and the error reporting in PHP is a bit dodgy in this area. I think it defaults to /tmp which is normally not what you want, especially in shared hosting environments.
Check this one:
http://blog.outsourcing-partners.com/2012/05/php-sessions-not-working-correctly-tips-and-tricks/
Also I notice you're running with PrestaShop in a subdirectory (chocolatsanssucre), but your nginx config is inconsistent about this, sometimes it uses the subdirectory and sometimes not. Please check the link that mdekker included further up for the correct nginx config.