If you can use server-side includes, use those (I forget the syntax). It may need the file extension changed to .shtml.
If you can't change the extension, configure the server to treat .html the same way as .shtml. But then, if you're going to do that, you might as well configure it to treat .html as the same as .php and use a PHP script.
You're basically asking "How can I use PHP without using PHP?"