Hello Arnaud, thanks for choosing Origami! The theme demo is running on php 7 with no issues, so there might be something else at play. Could you please try deactivating all plugins to see if any of those is to blame? If this does not bear fruit, please try activating the WP_DEBUG mode and paste here any error messages you see after refreshing the website.
Deprecated: Function get_currentuserinfo is deprecated since version 4.5.0! Use wp_get_current_user() instead. in /var/www/html/wp-includes/functions.php on line 5383