Get a taxonomy's terms in posts with another taxonomy's term

gistfile1.php

<?php
$base_taxonomy = 'pays';
$term_id = '1';

$required_taxonomy = 'villes';
$required_terms = array();
$required_terms_id = array();

$objects_in_tax = get_objects_in_term( $term_id, $taxonomy );

if( !empty( $objects_in_tax ) ) {
    if ( !is_wp_error( $objects_in_tax ) ) {
        foreach ( $objects_in_tax as $post_id ) {
            $required_terms = wp_get_object_terms( $post_id, $required_taxonomy );
            if ( !empty( $required_terms ) {
                if ( !is_wp_error( $required_terms ) ) {
                    foreach( $required_terms as $term ) {
                        $required_terms_id[] = $term->term_id;
                    }
                    $terms_id_unique = array_unique( $required_terms_id );
                }
            }
        }
    }
}
?>