You can add or remove CSS classes to the HTML element containing the sign-up form using the mc4wp_form_css_classes filter hook.

If we wanted to add a form-inline class to the form, we can use the following code:

add_filter('mc4wp_form_css_classes', function($classes) {
  $classes[] = 'form-inline';
  return $classes;

The above example adds the form-inline class which is used by Bootstrap. Please note that this filter adds the classes to the <div> element containing the form element, not to the form element itself.

If you want to add an ID to the form itself, you will need to add a little bit of information to your shortcode.