Drupal configuration on non root url (how to change $base_url)?
If your drupal installation resides on the webserver in a subfolder of the webroot for www.mymachine.fr, you can set the base path in the drupal site's .htaccess file.  


Find the line that reads # RewriteBase /drupal 
Uncomment it by deleting the "#" RewriteBase /drupal
Edit it to reflect your subpath/subfolder # RewriteBase /mydrupal


That block should look like this after the edits.

# Modify the RewriteBase if you are using Drupal in a subdirectory or in a
# VirtualDocumentRoot and the rewrite rules are not working properly.
# For example if your site is at http://example.com/drupal uncomment and
# modify the following line:
RewriteBase /mydrupal


Then, reset your .conf (vhost entry) to reflect just the top level website (code sample below resets to default .conf setup):

&lt;VirtualHost *:80&gt;
  ServerName mymachine.fr.mydrupal
  DocumentRoot /var/www

  ServerAdmin webmaster@localhost

  # Log configuration
  ErrorLog ${APACHE_LOG_DIR}/error.log
  CustomLog ${APACHE_LOG_DIR}/access.log combined

  &lt;Directory "/var/www"&gt;
      Options FollowSymLinks
      AllowOverride All
      Require all granted
  &lt;/Directory&gt;
&lt;/VirtualHost&gt;


This setup presumes that your top level domain does not have any redirection rules that forward/process all requests (such as the rules in an out-of-the-box Drupal or Wordpress .htaccess for processing requests with index.php)  If your top level domain has such a redirect rule in place, you may need to add another rule to exclude your mydrupal subdirectory.