Several points. A website created in Frontpage needs to be placed on a server with the Frontpage Extensions activated. You have already discovered that. Since I do not know your provider, you need to check the package you have. Very often it is a simple call or mail request and the extensions will be activated immediately.
If this is not possible, you will check on how to get out of your contract before you start spending money again. If you decide for a new hosting service, there is somewhere a place where you signed up for the name you have, and either on their website or via mail or via phone you can transfer your name to the new host with just supplying the new details.
If you received your name free of any charge while signing up during the start-up of the flat rate (like Force9 etc...and they do not keep their promise as hundreds will confirm) than you still can transfer but they will charge you for this.
If you do not get the extensions and you still do not want to spend the additional money than there is only one way, load your creation into Dreamweaver (or anything else) and alter and clean up the HTML and publish it this way.