FB is not defined javascript

This would be correct, you need to use FB after the JS SDK is initialized. That being said, you definitely don´t want to call FB.api in an infinite loop, so i removed that part:

<script>
    function init() {
        FB.api(
          '/l214.animaux',
          {"fields":"fan_count"},
          function(response) {
            alert(response.fan_count);
          }
        );
    }

    window.fbAsyncInit = function() {
      FB.init({
        appId      : 'your-app-id',
        xfbml      : true,
        version    : 'v2.5'
      });

      init();
    };

    (function(d, s, id){
      var js, fjs = d.getElementsByTagName(s)[0];
      if (d.getElementById(id)) {return;}
      js = d.createElement(s); js.id = id;
      js.src = "//connect.facebook.net/en_US/sdk.js";
      fjs.parentNode.insertBefore(js, fjs);
    }(document, 'script', 'facebook-jssdk'));
</script>

Make sure you run this from an actual server, don´t just open your HTML files in a browser without at least a local server.