//using jquery

$('form').on('submit', function(e) {

  if(grecaptcha.getResponse() == "") {

    e.preventDefault();

    alert("You can't proceed!");

  } else {

    alert("Thank you");

  }

});

<div class="g-recaptcha" data-sitekey="{YOUR-SITE-KEY-HERE}"></div>

<input type="hidden" class="hiddenRecaptcha required" name="hiddenRecaptcha" id="hiddenRecaptcha">

​