<form method="POST" class="form text-in" id="form0">
<div class="fields">
<div class="field" style="width: 177px;">
<div class="input">
<input required id="checkoutName" name="user_name" class="form-control text" type="text" placeholder="Имя *" value="" style="border-radius: 0px;">
</div>
</div>
<div class="field" data-type="phone" style="width: 177px;">
<div class="input">
<input required id="checkoutPhone" name="user_phone" class="form-control text" type="text" placeholder="Телефон *" value="" style="border-radius: 0px;">
</div>
</div>
</div>
<div class="macros-button">
<div class="btn-out full xs-none">
<div class="btn-inner">
<button class="btn font-text submit" id="uid19" type="submit">
<span class="text">Оформить заказ</span>
</button>
</div>
</div>
</div>
</form>
<script>
var uid19 = document.getElementById('uid19');
var form = document.getElementById('form0');
form.onsubmit = function(event){
event.preventDefault();
var data = new FormData(form);
var request = new XMLHttpRequest();
request.open('POST', 'АДРЕС_ОБРАБОТЧИКА.php');
request.send(data);
};
</script>тэг[атрибут=значение], у вас же там неведомо что, которое jQuery не понимает.