So I found at least a solution to get the fields from the “first” taxonomy.
It’d be great if someone could tell me how to randomize this!
<?php
global $post;
$terms = wp_get_post_terms($post->ID, 'movies', array('fields' => 'ids'));
//print_r($terms);
echo $terms[0];
?>
<?php echo get_field('director', 'movies_'.$terms[0]); ?>