How can I Add a variable PHP in the Menu Nav

You should never need a plugin to insert raw PHP code somewhere. There are always side effects you cannot see or fix easily.

Filter wp_nav_menu_objects instead, and add the parameter here to the URLs.

if ( ! empty ( $_GET['partenaire'] ) )
    add_filter( 'wp_nav_menu_objects', 'wpse_82194_add_param' );

/**
 * Add a parameter to item URLs.
 *
 * @wp-hook wp_nav_menu_objects
 * @param   array $items
 * @return  array
 */
function wpse_82194_add_param( $items )
{
    $out = array ();

    foreach ( $items as $item )
    {
        $item->url = add_query_arg( 'partenaire', $_GET['partenaire'], $item->url );
        $out[] = $item;
    }

    return $items;
}