First of all you need to get attachment ID for getting alt text..
Use this code to get that,
$img_id = get_post_thumbnail_id(get_the_ID());
Now add your code,
<?php $alt_text = get_post_meta($img_id , '_wp_attachment_image_alt', true); ?>
<h1 class="entry-title"><?php echo $alt_text; ?></h1>