<form role="form" class="Main__Form--contact" method="post" action="mail.php">
                <div class="Input__groups">
                    <input type="text" name="name" id="name" placeholder="Insira seu nome" required>
                </div>
                <div class="Input__groups">
                    <input type="email" name="email" id="email" placeholder="Insira seu e-mail" required>
                </div>
                <div class="Input__groups">
                    <input type="text" name="subject" id="subject" placeholder="Insira o assunto" required>
                </div>
                <div class="Input__groups">
                    <textarea name="message" id="message" rows="5" placeholder="Escreva sua mensagem" required></textarea>
                </div>
                <button type="submit" class="Button--blue Button_submit">Enviar</button>
            </form>

var form = $('.Main__Form--contact');
     form.submit(function(event){
     event.preventDefault();
     var form_status = $('<div class="Main__Form--status"></div>');

     var data = {
        name: $('#name').val(),
        email: $('#email').val(),
        subject: $('#subject').val(),
         message: $('#message').val()
    };

    $.ajax({
        url: $(this).attr('action'),
        type: "POST",
        dataType: "json",
        data: {'data': data},
        beforeSend: function(){
            form.prepend( form_status.html('<p class="text---white Column---left"><i class="fa fa-spinner fa-spin"></i> Enviando sua mensagem...</p>').fadeIn() );
        },
        success: function (d) {
        d = JSON.parse(d);
        if(d == 1){
                form_status.html('<p class="Column---left" style="color: #00ff00">Mensagem enviada com sucesso!</p>').delay(3000).fadeOut();
                $('#name').val("");
                $('#email').val("");
                $('#subject').val("");
                $('#message').val("");
            } else{
                form_status.html('<p class="Column---left" style="color: #ff0000">Ocorreu um erro ao tentar enviar a mensagem, tente novamente!</p>').delay(3000).fadeOut();
            }
        },
        error: function (xhr, status, error) {
            console.log(error);
        }
    });
});

<?php
   include_once "../PHPMailer/class.phpmailer.php";
   include_once "../PHPMailer/class.smtp.php";

   $data       = $_POST['data'];
   $name       = $data['name'];
   $subject    = $data['subject'];
   $message    = $data['message'];
   $email      = $data['email'];

   $mail = new PHPMailer();

   $mail->isSMTP();
   $mail->isHTML(true);
   $mail->Mailer = 'smtp';
   //$mail->SMTPDebug = 2;
   $mail->SMTPAuth = true;
   $mail->CharSet = 'UTF-8';
   $mail->SingleTo = true;

   //configuração do email
   $mail->Port = '587';
   $mail->Host = 'xxxxx';
   $mail->Username = 'xxxx@xxxx.com.br';
   $mail->Password = 'xxxxxx';
   $mail->From     = 'xxx@xxx.com.br';
   $mail->FromName = 'Atendimento';

   $destinatario = 'xxxx@xxxx.com';
   $mail->addAddress($destinatario);
   $mail->addReplyTo($email);

   $mail->Subject = $subject;

   $remetente = '-=-=-=- Formulário de Contato -=-=-=-';
   $remetente = $remetente . '<br> Enviado por: '. $name;
   $remetente = $remetente . '<br> E-mail: '. $email;

   $documento = $message. ' <br><br><br><br>' . $remetente;
   $mail->Body = $documento;

   if (!$mail->send()) {
       //echo 'Erro:' . $mail->ErrorInfo;
       echo json_encode(0);
       exit;
   }
   else {
    echo json_encode(1);
    exit;
   }