WordPress Ajax JSON success return no being recognized

You are not giving the action name to your AJAX call. In WordPress, you have to give an action name, the same name you give whatever is after wp_ajax_ and wp_ajax_nopriv_

In this case, the AJAX call should work if you change the data: inside your AJAX call, for this:

data: {action: "contactform_action", values: $('#contact-form').serialize()}

Then retrieve the values of the form with $_POST["values"]; in your php function.