I used to get my website to simply email me course registrations. Then I had to copy/paste the information into my database. Now the web site has a MySQL backend and my FileMaker Pro database links directly to that. That would be a longer term solution for you.
Obviously your emails from your web site will have a consistent format at least in the data area. So what you could do is to copy/paste the entire data block from the email into a global field and use a script to parse it out from there into a new record.
I still get emails like this for newsletter subscriptions:
Joe Bloggs has subscribed to the newsletter.
Company: His Company Pty Ltd
This data can be easily parsed out into separate name, email and company fields.
If you want help with that, post a fictitious sample data in the exact format you get it in your email. I will script a solution given that data is in a global field.
You could set Mail rules to run an Applescript automatically on reception of form data. The script would parse the received data, create a new record in Filemaker and populate it.