the_tags : can we insert a class

Yes, it is possible.

<?php
$post_tags = get_the_tags();
if ($post_tags) {
  foreach($post_tags as $tag) {
    echo '<a href="'; echo bloginfo();
    echo '/?tag=' . $tag->slug . '" class="' . $tag->slug . '">' . $tag->name . '</a>';
  }
}
?>

The code is from another answer on Stack Overflow, see here for the source and more info