Sounds like you install WordPress on a subdirectory (/multi) and on localhost? Can you log in the main site admin: /multi/wp-admin?
The error is to do with “permission to access the requested directory”, it’s probably not to do with WordPress settings/config.
Check your WP installation again for potential missing steps (which might cause the permission issue) with this: https://www.digitalocean.com/community/tutorials/how-to-install-linux-apache-mysql-php-lamp-stack-on-debian
and this: https://www.digitalocean.com/community/tutorials/how-to-install-wordpress-on-debian-7
(I do exactly as the guide and don’t have any error when activate multisite, WP4.7 on Debian 8.6)