PHP contact page setup

Question

I set up my PHP contact page setup, but the message cannot be sent.

It seems like my php codes are corrects.

Please find below the contact.php page's code:

<!-- Configuration-->

<?php require_once("../resources/config.php"); ?>


<!-- Header-->
<?php include(TEMPLATE_FRONT .  "/header.php");?>


     <!--Navigation -->

<?php include(TEMPLATE_FRONT .  "/top_nav.php");?>

         <!-- Contact Section -->

        <div class="container">
            <div class="row">
                <div class="col-lg-12 text-center">
                    <h2 class="section-heading">Contact Us</h2>
                    <h3 class="section-subheading text-muted">

                        <?php display_message(); ?>

                    </h3>
                </div>
            </div>
            <div class="row">
                <div class="col-lg-12">
                    <form name="sentMessage" id="contactForm" method="post">

                    <?php send_message(); ?>


                        <div class="row">
                            <div class="col-md-6">
                                <div class="form-group">
                                    <input type="text" name="name" class="form-control" placeholder="Votre prénom *" id="name" required data-validation-required-message="Please enter your name.">
                                    <p class="help-block text-danger"></p>
                                </div>
                                <div class="form-group">
                                    <input type="email" name="email" class="form-control" placeholder="Votre email *" id="email" required data-validation-required-message="Please enter your email address.">
                                    <p class="help-block text-danger"></p>
                                </div>
                                <div class="form-group">
                                    <input type="text" name="subject" class="form-control" placeholder="Votre sujet *" id="subject" required data-validation-required-message="Please enter a message.">
                                    <p class="help-block text-danger"></p>
                                </div>
                            </div>
                            <div class="col-md-6">
                                <div class="form-group">
                                    <textarea name="message" class="form-control" placeholder="Votre message *" id="message" required data-validation-required-message="Please enter a message."></textarea>
                                    <p class="help-block text-danger"></p>
                                </div>
                            </div>
                            <div class="clearfix"></div>
                            <div class="col-lg-12 text-center">
                                <div id="success"></div>
                                <button type="submit" name="submit" class="btn btn-xl">Send Message</button>
                            </div>
                        </div>
                    </form>
                </div>
            </div>
        </div>

    </div>
    <!-- /.container -->
<?php include(TEMPLATE_FRONT .  "/footer.php");?>

And below please find the functions.php code I used:

function send_message() {

    if(isset($_POST['submit'])){

        $to           = "someEmailaddress@gmail.com";
        $from_name    =     $_POST['name'];
        $subject      =     $_POST['subject'];
        $email        =     $_POST['email'];
        $message      =     $_POST['message'];


        $headers = "From: {$from_name} {$email}";


        $result = mail($to, $subject, $message, $headers);

            if(!$result) {

                set_message("Désolés, nous n'avons pas pu envoyer votre message");
                redirect("contact.php");
            } else {

                set_message("Votre message a bien été envoyé");
                redirect("contact.php");
        }

    }

Is there anyone who knows where is the error?