I'm trying to develop an app with Microsoft's Visual Basic Express 2008 to run on the .net framework 1.0. Is there something I can download to do this or do I have to require the latest framework to be downloaded?
No:
You could still compile against .NET 1.0 or .NET 1.1 if you've got those installed by running the command line tools directly - but you won't be able to use Visual Studio to build without a fair chunk of work, IIRC. (I seem to remember there is a tool to allow it, but I don't know how well it works, and I doubt that it's supported now.)