Your error referes back to your first line ofr validation -
if( $_POST['form_name'] != '' AND $_POST['form_email'] != '' AND $_POST['form_subject'] != '' )
which tells you that one of your required fields is empty. The way to solve this is to go back one page to your html form and carry out all the validations in their respective text elements. If any element is empty, do not POST the form, let the user complete the information as required. When all validations were passed, then POST your form and your code should run fine.