Displaying shortcode output through Options Framework

You should check out the WordPress function do_shortcode().

You can use it to generate the shortcodes, in a string variable, like this :

<?php echo do_shortcode( $content ) ?>

So in your case, please try:

<?php 
  if ( of_get_option('footer_contact_form') ) {
      echo do_shortcode( of_get_option('footer_contact_form') ); 
 }
?>