How can I give CPT archive correct body class?

There’s filter called body_class for that.

function my_own_body_classes($classes) {

    // Add Classes to body if the post type archive is 'publikasjoner'
    if ( is_post_type_archive( 'publikasjoner' ) ) {
        $classes[] = 'publikasjoner-archive';
    }
    // Go for other posts types here


    return $classes;
}
add_filter('body_class', 'my_own_body_classes');