Formulář s přílohou

<form method="POST" action="contact.php" id="formular">
                                <input autocomplete="off" type="text" name="fullname" placeholder="Jméno a příjmení" class="kontakt-single clrthis" required><br>
                                <input autocomplete="off" type="email" name="email" placeholder="Email" class="kontakt-double clrthis" style="float: left;" required>
                                <input autocomplete="off" type="text" name="phone" placeholder="Telefon" class="kontakt-double clrthis" style="float: right;" required><br>
                                <textarea name="message" placeholder="Zpráva" class="kontakt-textarea clrthis" required></textarea><br>
                                <input type="file" name="soubor"><br>
                                <input type="submit" name="submit" value="Odeslat zprávu" class="kontakt-submit">
                            </form>

                            <script type="text/javascript">
                                $("#formular").submit(function(e) {
                                    e.preventDefault();

                                    var form = $(this);
                                    var url = form.attr('action');

                                    $.ajax({
                                          type: "POST",
                                          url: url,
                                          data: form.serialize(),
                                          success: function(data)
                                          {
                                            $("#formular").prepend(data);

                                            var areas = document.getElementsByClassName("clrthis");

                                            for(var i = 0; i < areas.length; i++){
                                                areas[i].value = "";
                                            }
                                        }
                                    });
                                });
                            </script>

<?php
    include_once "headers.php";
    include_once "db.php";

    function check_if_empty($input){
        if(empty($input))
            return "-";
        else
            return $input;
    }

    if((!empty($_POST["email"]) || !empty($_POST["phone"])) && !empty($_POST["fullname"]) && !empty($_POST["message"])){
        $to      = "prijemce@email.cz";
        $subject = "Dotaz";

        $message = htmlspecialchars(check_if_empty($_POST["fullname"]))."<br>";
        $message .= htmlspecialchars(check_if_empty($_POST["email"]))."<br>";
        $message .= htmlspecialchars(check_if_empty($_POST["phone"]))."<br><br>";
        $message .= str_replace("\n", "<br>", check_if_empty($_POST["message"]));

        $headers = "Content-Type: text/html; charset=UTF-8\r\n";
        $headers .= "From: odesilatel@email.cz";

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

        $stmt = $connection->prepare("INSERT INTO messages (id, fullname, email, phone, message) VALUES (null, ?, ?, ?, ?)");
        $stmt->bind_param("ssss", $fullname, $email, $phone, $message);

        $fullname = $connection->real_escape_string(htmlspecialchars(check_if_empty($_POST["fullname"])));
        $email = $connection->real_escape_string(htmlspecialchars(check_if_empty($_POST["email"])));
        $phone = $connection->real_escape_string(htmlspecialchars(check_if_empty($_POST["phone"])));
        $message = $connection->real_escape_string(htmlspecialchars(check_if_empty($_POST["message"])));

        if($stmt->execute())
            echo "Děkujeme, na Vaši zprávu odpovíme nejpozději do 24 hodin.";
        else
            echo "Omlouváme se, ale při zpracování došlo k chybě.";
    }
    else {
        echo "Omlouváme se, ale nebyly správně zadané údaje.";
    }
?>