Freeform Success Notice in Template
You can add a param to your returnUrl in the form composer then check the template for the param.

For example:

You redirect to /contact?success

{% set successParam = craft.request.getParam('success') %}
{% if successParam is not null %} 
  &lt;p&gt;Hooray! Success!!&lt;/p&gt;
{% endif %}


Another option is to Ajax submit your form and just have a modal or something on a succes submit. An example of an Ajax submit can be found in the official freeform docs here.