Display Custom Field Value on Admin Page Column

The main errors where the missing of the $post_ID parameter in page_template_field and using $custom_field_id instead of $post_ID.

Anyway, this works and is simpler:

add_filter('manage_pages_columns', 'column_page');
function column_page($defaults) {
    $defaults['column_template'] = 'Page Template';
    return $defaults;
}

add_action('manage_pages_custom_column','column_page_template',10,2);
function column_page_template($column_name, $post_ID) {
    if ($column_name == 'column_template') {
        $custom_field_values = get_post_meta($post_ID,'page_template');
        if (!empty($custom_field_values)) {
            echo '<p> '. join(', ',$custom_field_values) .' </p>';
        }
    }
}