Open the main web in FP 2003 and create a new folder under the root - that's the main folder at the top of the folder view. Call the folder anything you like - 'testweb' would be an idea.
Now, right click on the new folder and select 'convert to web' from the menu that appears. You'll see a warning about links and pages withing the subweb but ignore that and go ahead. Now open the subweb folder and create your new version of the site, as if you were starting from scratch. Make sure that you put a copy of all images into the image folder - don't reference them from the folder in the main web.
When you've finished, publish the site to the server, and test it by typing a url to one of the pages. This would take the form of:
h t t p:// w w w. yourmaindomain.co.uk/testweb/carnival_queen.html or whatever your page name is. I've added spaces here to stop the 'click here' link appearing.