But if you don’t have permalinks set up, it won’t work. Check whether or not they are set up and see if this page really exists. Otherwise, try referencing it to some page you do know exists for sure, and add the extension to it, like this:
I encountered the same issue, and it has to do with the form field names. I believe WordPress is interpereting either a POST or GET key value of ‘name’ as a post name to determine what wordpress page to show (resulting in a 404 error in most cases).
To verify if this is the issue, put in the slug of a post (like ‘contact-php’) in the name field, submit the form and see what happens (If it is a valid page/post slug, it should take you to that page).