Display taxonomy of a post in Wordpress - php

Question

I have a page where all my WP posts are displayed. The category of the post displays fine but when I try to also display the taxonomy, it doesn't work.
This is working :
<span><i class="fa fa-list"></i><?php $categories = get_the_category();
$separator = ", ";
$output = '';
if($categories){
if($link_on_cat == "yes"){
foreach($categories as $category){
$output .= '' . $category->cat_name . '' . $separator;
}
} else {
foreach($categories as $category){
$output .= $category->cat_name . $separator;
}
}
echo trim($output, $separator);
} ?></span>
This is not working :
<span><i class="fa fa-list"></i><?php $categories = get_the_category();
$separator = ", ";
$output = '';
global $post, $post_id;
$post_type = $post->post_type;
$taxonomies = get_object_taxonomies($post_type);
if($categories){
if($link_on_cat == "yes"){
foreach($categories as $category){
$output .= '' . $category->cat_name . '' . $separator;
}
foreach ($taxonomies as $taxonomy) { $out .= "<li>".$taxonomy.": "; $terms = get_the_terms( $post->ID, $taxonomy );
if ( !empty( $terms ) ) {
foreach ( $terms as $term )
$out .= ''.$term->name.' ';
} }
} else {
foreach($categories as $category){
$output .= $category->cat_name . $separator;
}
}
echo trim($output, $separator);
} ?></span>
Of course I'm doing something wrong, but what ?