JSFiddle - React, Tailwind, and code Playground

HTML

<form>
  <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" name="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" name="phone" type="tel" autocomplete="tel" required>
  <br>
  <input class="btn btn-cta appointment-block__input" type="submit" value="Записаться на бесплатный приём">
</form>

JavaScript

for (var i = 0; i < forms.length; i++) {
  forms[i].onsubmit = function (form) {

    return function() {

      var xhr = new XMLHttpRequest();

      xhr.open("POST", "sendemail.php", true);
      xhr.send(new FormData(form));

      modalThx.classList.add("modal-thx--show");

      return false;
    };

  }(forms[i]);
}