联系表单不工作 - php文件返回“else”失败的响应

I have tried looking in similar questions posted here, but cannot find an answer (got about 1900 questions popping up).

I have a contact form on a page at a site I am creating on the webpage hosting site https://www.one.com/en/

Here is the form on the page contact/contact.shtml

<form action="contact/mail.php" method="post"><br>
    Your name<br>
    <input type="text" name="cf_name"><br>
    Your e-mail<br>
    <input type="text" name="cf_email"><br>
    Message<br>
    <textarea name="cf_message"></textarea><br>
    <input type="submit" value="Send">
    <input type="reset" value="Clear">
</form>

Here is the content of the contact/mail.php file

<?php
    $field_name = $_POST['cf_name'];
    $field_email = $_POST['cf_email'];
    $field_message = $_POST['cf_message'];
    $mail_to = 'clashton@gmail.com';
    $subject = ' Contact Form '.$field_name;
    $body_message = 'From: '.$field_name."
";
    $body_message .= 'E-mail: '.$field_email."
";
    $body_message .= 'Message: '.$field_message;
    $headers = 'From: '.$field_email."
";
    $headers .= 'Reply-To: '.$field_email."
";
    $mail_status = mail($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.shtml';
    </script>
    <?php
    }
    else { ?>
    <script language="javascript" type="text/javascript">
        alert('Message failed. Please, send an email to clashton@gmail.com');
        window.location = 'contact.shtml';
    </script>
    <?php
    }
?>

When I try to send a message a window pops up containing the error message "Message failed. Please, send an email to clashton@gmail.com". In other words the "else" action is happening.

If it seems that this question has a trivial answer, please keep in mind that I am completely new at this.

Thanks for any help.