Sending the Email is the easy part. Any formmail script handle that with little or no modification. The tricky part is combining these two functions with a single form submission.
The alternative would be to create an intermediate script that would handle the mailing and then proceed to submit the form data to the payment processor. I had to do something similar not long ago and ran into some HTTP security issues. You can't, for example, use method="post" and have the destination script respond with a 301 or 302 redirect. I ended up having the formmail script display a "Continue" button which was a part of a form that submitted the user's data to the payment processor. It was clumsy, but I was under a tight deadline and it worked.