You don’t need to know the file names before, you’ll have access to them.

I saw you using $subject = $_POST['subject']; – this means the subject will be the value of the input with the name of “subject”. In your case, this one :

<input id="subject" class="form-control" name="subject" type="text" /></div>

We can use the same logic to get the files, but instead of $_POST, we’ll look in $_FILES. Your file form has the name of “image”, so the location will be $_FILES[‘image’]. We can then handle the upload.
I wrote a small example to show you how you would do that, but you should add some validation on it, depending on your use case :

if(isset($_POST['submit']) && strpos($_SERVER['HTTP_REFERER'], 'https://example.com/custom-file/') !== false) {
    $to = 'contact@mail.com'; // Replace with your own email address
    $subject = $_POST['subject']; // Get the value of the subject field from the form
    $message = "Name: " . $_POST['name'] . "<br><br>";
    $message .= "Email: " . $_POST['email'] . "<br><br>";
    $message .= "Message: " . $_POST['message'] . "<br><br>";

    $headers = array('Content-Type: text/html; charset=UTF-8');

    // Handle the uploaded file
    if ($_FILES['image']['error'] == UPLOAD_ERR_OK) {
        $tmp_name = $_FILES['image']['tmp_name'];
        $filename = basename($_FILES['image']['name']);
        $upload_dir = wp_upload_dir();
        $destination = $upload_dir['basedir'] . "https://wordpress.stackexchange.com/" . $filename;

        // Move the file to the uploads directory
        if (move_uploaded_file($tmp_name, $destination)) {
            $attachments = array($destination);
        }
    }

    if (wp_mail($to, $subject, $message, $headers, $attachments)) {
        wp_redirect('/thank-you-contact-form-sent'); // Replace with the URL of your thank-you page
        exit();
    } else {
        wp_redirect('/sorry-contact-form-not-sent'); // Replace with the URL of your sorry page
        exit();
    }
}