blemieux42,
I think you have a misunderstanding about CoffeeCup software. I build my websites using CoffeeCup software. Think of it as building a house using a hammer and nails. The house is not a hammer and nails. My website is not CoffeeCup software.
I do RUN some CoffeeCup software such as the photo gallery, and the RSS News Flash, but the site is just HTML code that could be written with MS Notepad (or any text editor).
What you would do is set the forum software in a folder on your website, and then have a link to access your forum. I have a Wordpress blog, and it is created using Wordpress. I have it in a separate subdirectory and maybe I will insert a link on my site to lead friends and family to the blog.
The forum software you looked at (phpBB) will have specific requirements for your server. If you elect to use phpBB, your server must have PHP installed. I think most servers have PHP running, but then I have not seen all servers

so could be wrong. Check the information from your host and you may find the information you need. If you don't find what you need, ask here and someone will likely be able to tell you how to get the needed information.
Hope I haven't muddied the waters too much.