Formulaire de contact et Recaptcha invisible

<?php
session_start();//on démarre la session
// $errors = [];
//On check les infos transmises lors de la validation
  if(!empty($errors)){ // si erreur on renvoie vers la page précédente
  $_SESSION['errors'] = $errors;//on stocke les erreurs
  $_SESSION['inputs'] = $_POST;
  header('Location: contact.html');
  }else{
  $_SESSION['success'] = 1;
  $headers  = 'MIME-Version: 1.0' . "\r\n";
  $headers .= 'Content-type: text/html; charset=utf-8' . "\r\n";
  $headers .= 'FROM:' . htmlspecialchars($_POST['email']);
  $to = 'contact@6ro.fr'; // Insérer votre adresse email ICI
  $subject = 'Message envoyé par ' . htmlspecialchars($_POST['name']);
  $message_content = '
  <table>
  <tr>
  <td><b>Emetteur du message:</b></td>
  </tr>
  <tr>
  <td>'. $subject . '</td>
  </tr>
  <tr>
  <td><b>Contenu du message:</b></td>
  </tr>
  <tr>
  <td>'. htmlspecialchars($_POST['message']) .'</td>
  </tr>
  </table>
  ';

/** reset des données envoyées **/
unset($_POST);

/** envoi du courriel **/
if (mail($to, $subject, $message_content, $headers)) {
$frontMsg = 'You mail was correctly sent, thank you!';
$frontLink = '<a href="home.html">Return Home</a>';
} else {
$frontMsg = 'An error has occurs. Your message don\'t have been sent!';
$frontLink = '<a href="contact.html">Return Form</a>';
}

/** Affichage du message pour l'utilisateur **/
echo '<div>', $frontMsg, '</div>';
echo '<p>', $frontLink, '</p>';
?

$(function () {

    window.verifyRecaptchaCallback = function (response) {
        $('input[data-recaptcha]').val(response).trigger('change')
    }

    window.expiredRecaptchaCallback = function () {
        $('input[data-recaptcha]').val("").trigger('change')
    }

    $('#contact-form').validator();

    $('#contact-form').on('submit', function (e) {
        if (!e.isDefaultPrevented()) {
            var url = "contact.php";

            $.ajax({
                type: "POST",
                url: url,
                data: $(this).serialize(),
                success: function (data) {
                    var messageAlert = 'alert-' + data.type;
                    var messageText = data.message;

                    var alertBox = '<div class="alert ' + messageAlert + ' alert-dismissable"><button type="button" class="close" data-dismiss="alert" aria-hidden="true">&times;</button>' + messageText + '</div>';
                    if (messageAlert && messageText) {
                        $('#contact-form').find('.messages').html(alertBox);
                        $('#contact-form')[0].reset();
                        grecaptcha.reset();
                    }
                }
            });
            return false;
        }
    })
});