You can try a simple trick.
what is does is if a spammer loads your form he will submit to
/contact-alt.php then you'd use this script to block him.
<form name="contact_form" method="post" action="/contact-alt.php" enctype="multipart/form-data" accept-charset="UTF-8" onsubmit="this.action='contact.php';">
the rest of your form
do let me know if you have any questions.