If ALL of your files are located under www.sebmayer.com/travaux then this URL is incorrect:
$_CONF['site_url'] = 'http://www.sebmayer.com/travaux';
It should be this:
$_CONF['site_url'] = 'http://www.sebmayer.com/travaux/public_html';
Once you correct $_CONF['site_url'], then this URL will be off:
$_CONF['site_admin_url'] = $_CONF['site_url'] . '/public_html/admin';
and should be changed to this:
$_CONF['site_admin_url'] = $_CONF['site_url'] . '/admin';
If you want to bring up your site by typing: 'http://www.sebmayer.com/travaux' instead of 'http://www.sebmayer.com/travaux/public_html', then place the files inside Geeklog's public_html directory right into your travaux directory. Then take the remaining files (config.php, /system, /language, etc) and place them in a non-public area on your server.
I'm guessing '/home/sebmayer/www/' is the path for 'http://www.sebmayer.com/' . If I'm wrong, then please let me know. If I'm right, then your non-public files would go under '/home/sebmayer/' and the paths would like this instead:
$_CONF['path'] = '/home/sebmayer/';
$_CONF['path_html'] = $_CONF['path'] . 'public_html/';
$_CONF['path_system'] = $_CONF['path'] . 'system/';
$_CONF['path_log'] = $_CONF['path'] . 'logs/';
$_CONF['path_language'] = $_CONF['path'] . 'language/';
$_CONF['rdf_file'] = $_CONF['path_html'] . 'backend/geeklog.rdf';
$_CONF['backup_path'] = $_CONF['path'] . 'backups/';
$_CONF['site_url'] = 'http://www.sebmayer.com/travaux';
$_CONF['site_admin_url'] = $_CONF['site_url'] . '/admin';
$_CONF['layout_url'] = $_CONF['site_url'] . '/layout/' . $_CONF['theme'];
$_CONF['path_themes'] = $_CONF['path_html'] . 'layout/';
$_CONF['path_layout'] = $_CONF['path_themes'] . $_CONF['theme'] .'/';