Presatashop ajax Captcha validation

[Jluis]

Hello ,
i have installed a recaptcha module , it works fine withe default contact-form.tpl .When i'm building a specific tpl contact form containing a captcha validation , when submitting the button , it doesn't make the validation either the captcha is verified or not .Below is my contact.tpl file ; what was missing please? is it a ajax issue ?

<div class="raw contactez-nous-index parallax-container" 
    		data-parallax="scroll" data-bleed="10" data-speed="0.2" 
    		data-image-src="img/bg-contact.jpg" 
    		data-natural-width="1400" data-natural-height="1400">

    	<div class="container contact-index">
    		<img src="img/envolope-contact.png" alt="CONTACT-US">
    		<p class="titre-equip">CONTACT-US</p>
    		
    		<div class="formulaire-contact-index">
    		
    			<form  class="f-index contact-form-box" name="f-index" id="f-index" method="POST" accept-charset="utf-8">
    			<div class="alert alert-danger " style="width:50%;margin:10px auto;"></div>
    			<div class="alert alert-success" style="width:50%;margin:10px auto;"></div>
    				<input class="form-index-champs champs-1" type="text" id="first_last_name" name="first_last_name" value="" placeholder="Nom - Prénom">
    				<input class="form-index-champs champs-2" type="text" id="campany" name="campany" value="" placeholder="Sociéte">
    				<input class="form-index-champs champs-2" type="email" id="email"name="email" value="" placeholder="E-mail">
    				<input class="form-index-champs champs-3" type="phone" id="phone" name="phone" value="" placeholder="Téléphone">
    				<textarea class="text-area-msg" id="message" name="message" placeholder="Message"></textarea>
    				<div id="captcha-box" style="margin: 22px auto;float: none;width: 304px;"></div>
    			</form>
    			<button class="env-btn"  type=""><p class="envy">SEND</p></button>
    		</div>
    	</div>	
    </div>
    <script>
    $(document).ready(function()
    {
    $('.alert-danger').hide();
    $('.alert-success').hide();

    $('.env-btn').on('click',function(){
    var name=$('#first_last_name').val();
    var email=$('#email').val();
    var phone=$('#phone').val();
    var campany=$('#campany').val();
    var message=$('#message').val();
    $.ajax({
          type: 'POST',
    			headers: { "cache-control": "no-cache" },
    			url: baseUri + '?rand=' + new Date().getTime(),
    			async: true,
    			cache: false,
    			dataType: 'json',
    			data: 'controller=contact&ajax=true&small_contact=true'
    			+ '&first_last_name='+name
    				+ '&email='+email	
    				+ '&campany='+campany
    				+ '&phone='+phone
    				+ '&message='+message
    				+ '&token='+static_token,
    			success: function(jsonData)
    			{
    				if(jsonData.result){
    			$('.alert-success').show();
    			$('.alert-success').html('');
    			$('.alert-danger').hide();
    			$('.alert-danger').html('');
    			$('.alert-success').prepend('<p>'+jsonData.result+'</p>');
    			}
    			if(jsonData.error){
    			
    			$('.alert-danger').show();
    			$('.alert-success').html('');
    			$('.alert-success').hide();
    			$('.alert-danger').html('');
    			$('.alert-danger').prepend('<p>'+jsonData.error+'</p>');
    			
    			}
    			}
    			
    			
    });
    });
    });

    </script>