How can I change/edit the email template?

Is there any way to change what is sent/added during the "forward" process when forwarding contract copies?

When you say "forward process" did you mean the email notifications you receive? If you want to edit/change/modify the email template, just follow the guide I'm linking below. You can change the actual email body upon your discretion.

Complete guide: How-to-Edit-the-Email-Template-for-Notifications-and-Autoresponders