Maybe you could use a filter to add the current language of the website to the body class.
add_filter('body_class', 'language_in_body_classes');
function language_in_body_classes($classes) {
$classes[] = get_bloginfo('language');
return $classes;
}
Edit : maybe I misunderstood what you wanted. There is actually a language_attributes filter but I do not think it would be very standard to add classes to the html language attr.