Activating Contact Form - php

Question

I don't know any PHP at all so I researched a couple hours to try and get my contact form to actually save and send the inputs to my email. As of right now, I'm getting an error Failed to load resource: the server responded with a status of 405 (). Here is the contact form code and also PHP file code. They are located in the root directory, named index.html and contact.php. I'm using the template html5up.net/strata.
<form method="post" action="contact.php" id="form" class="contact-form">
<div class="row uniform 50%">
<div class="6u 12u$(xsmall)"><input type="text" name="cf_name" id="name" placeholder="Name" /></div>
<div class="6u$ 12u$(xsmall)"><input type="email" name="cf_email" id="email" placeholder="Email" /></div>
<div class="12u$"><textarea name="cf_message" id="message" placeholder="Message" rows="4"></textarea></div>
</div>
<ul class="actions">
<li><input type="submit" value="Send Message" class="special"/></li>
</ul>
</form>
contact.php
<?php
$field_name = $_POST['cf_name'];
$field_email = $_POST['cf_email'];
$field_message = $_POST['cf_message'];
$mail_to = 'simonchangwong#gmail.com';
$subject = 'Message from a site visitor '.$field_name;
$body_message = 'From: '.$field_name."\n";
$body_message .= 'E-mail: '.$field_email."\n";
$body_message .= 'Message: '.$field_message;
$headers = 'From: '.$field_email."\r\n";
$headers .= 'Reply-To: '.$field_email."\r\n";
$mail_status = mail($mail_to, $subject, $body_message, $headers);
if ($mail_status) { ?>
<script language="javascript" type="text/javascript">
alert('Thank you for the message. We will contact you shortly.');
window.location = 'contact_page.html';
</script>
<?php
}
else { ?>
<script language="javascript" type="text/javascript">
alert('Message failed. Please, send an email to gordon#template-help.com');
window.location = 'contact_page.html';
</script>
<?php
}
?>