I finally managed to make Strapi work on a managed hosting 
Here is my setup:
.env :
HOST=0.0.0.0
PORT=1337
PUBLIC_URL=https://my.domain.com
.htaccess :
RewriteEngine On
RewriteRule ^$ http://localhost:1337/ [P]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ http://localhost:1337/$1 [P]