In order to have a form start using the new system, you have to tell it to stop using the old system. The old form will continue to work using the old system until it is edited. Once you edit the form you also need to change the script.

The Form Action field (at the top of the DCR) tells the form where to send it's data. Form_contact/form_contact.php is the old system, and as long as that is set, the old system will continue to be used. The NEW system needs to send it's data directly back to the page it came from. To do this, you will need to remove the FORM ACTION entirely and just leave it blank.