Hook in parent theme Menu function

You just need to fire the original one, not to remove.

add_filter( 'original_theme_menus', 'your_theme_menus', 1, 1 );
function your_theme_menus( $menus )
{
    $new_menu = array(
        'footer' => __( 'Footer Menu', 'theme-domain' )
    );
    $menus = $menus + $new_menu;

    return $menus;
}