I did not use the Post Types Order, but put the function from kakaroto84 in my functions.php.
Now my code looks like this:
<?php
$child_pages = get_field('child_pages');
objectRSort($child_pages, 'menu_order');
if( $child_pages ): ?>
<ul class="subpages">
<?php foreach( $child_pages as $post): ?>
<?php setup_postdata($post); ?>
<li>
<a href="<?php the_permalink(); ?>"><?php the_title(); ?></a>
</li>
<?php endforeach; ?>
</ul>
<?php wp_reset_postdata(); ?>
<?php endif; ?>
Thank you kakaroto84!