Require User to click google's new recaptcha before form submission

You can check the textarea field with id g-recaptcha-response. You can do as following:

$("form").submit(function(event) {

   var recaptcha = $("#g-recaptcha-response").val();
   if (recaptcha === "") {
      event.preventDefault();
      alert("Please check the recaptcha");
   }
});

Hope this helps you.

A vanilla JavaScript implementation using parts of both Ankesh's and Lammert's solution:

var form = document.getElementById('ctct-custom-form');
form.addEventListener("submit", function(event){
    if (grecaptcha.getResponse() === '') {                            
      event.preventDefault();
      alert('Please check the recaptcha');
    }
  }
, false);

Credit to for form submit listener code: How can I listen to the form submit event in javascript?

grecaptcha.getResponse() - Returns the response for the Recaptcha. You can check this in condition such as

grecaptcha.getResponse(opt_widget_id) === ""

Optional widget ID, defaults to the first widget created if unspecified.

Ref: https://developers.google.com/recaptcha/docs/display