Contact Form HTML-PHP

Hola! Espero estén muy bien todos, tengo un problema con un formulario de contacto, les pongo el código también les anexo mi PHP, que no me funciona.
Les agradezco mucho la ayuda!

HTML:


<div class="sec-title text-center wow animated fadeInDown">
<h2>Contacto</h2>
<p>Déjanos tus comentarios</p>
</div>

<div class="col-md-7 contact-form wow animated fadeInLeft">


<form action="contact.php" method="post" class="tm-contact-form">
<div class="form-group">
<input name=”cf_name” type="text" id="contact_name" class="form-control" placeholder="Nombre..." />
</div>
<div class="form-group">
<input name=”cf_email” type="text" id="contact_email" class="form-control" placeholder="Email..." />
</div>
<div class="form-group">
<textarea name=”cf_message” id="contact_message" class="form-control" rows="8" placeholder="Mensaje..."></textarea>
</div>

<button type="submit" id="submit" class="btn btn-blue btn-effect">Enviar</button>

</form>
</div>




PHP:

<?php
$field_name = $_POST['cf_name'];
$field_email = $_POST['cf_email'];
$field_message = $_POST['cf_message'];

$mail_to = 'email@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 = 'MIME-Version: 1.0' . "\r\n";
$headers .= 'Content-type: text/html; charset=iso-8859-1' . "\r\n";
$headers = 'From: '.$field_email."\r\n";
$headers .= 'Reply-To: '.$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 = 'index.html';
</script>
<?php
}
else { ?>
<script language="javascript" type="text/javascript">
alert('Message failed. Please, send an email to email@gmil.com');
window.location = 'index.html';
</script>
<?php
}
?>