JSFiddle - React, Tailwind, and code Playground

HTML

<!--header-->
<script type="text/javascript" src="js/jquery.js"></script>
<script type="text/javascript" src="js/ajax.js"></script>

<!--body-->
  <label class="appointment-block__label" for="appointment-block__inputs-name">Ваше имя</label>
  <br>
  <input class="appointment-block__input appointment-block__name" id="appointment-block__inputs-name" type="text" autocomplete="on" required>
  <br>
  <label class="appointment-block__label" for="appointment-block__inputs-tel">Номер телефона</label>
  <br>
  <input class="appointment-block__input appointment-block__tel" id="appointment-block__inputs-tel"type="tel" autocomplete="tel" required>
  <br>
  <input class="btn btn-cta appointment-block__input" id="appointment-block__inputs-submit" type="button" value="Записаться на бесплатный приём">

JavaScript

// js/ajax.js

$(function () {
    $("#appointment-block__inputs-submit").click(function() {
        var name = $("#appointment-block__inputs-name").val();
        var tel = $("#appointment-block__inputs-tel").val();

        $.post("sendemail.php", {
            name: name,
            tel: tel
        });
    });
});