If you're using an "active" server technology like JSP (Java) or ASP.NET, or other HTTP-enabled technology, you could write code on the server side to populate forms with Request data received. Then, from FMP, you do an INSERT FROM URL and pass the form variables you want to display.
I haven't tested this in .NET, but in Java, it would be a straightforward task (JSP, Servlet or framework like Spring).
Depending on the configuration (Intra-vs-Internet), you would need extra validation for incoming Requests.
Depending on the site and how the form works, you might be able to use Insert From URL and POST the Data straight from FileMaker. No need (perhaps) to use any server side code.
Yes it does depend if the "receiving" web site allows passing the values (with POST or GET) and will have a method to populate the form fields. Some will block such an action. It prevents the spammers and non-human "posters" and malicious hackers.