There is no specific import that will clean up. I suspect you will need to just import the HTML files and then clean out any HTML that is ForeHelp specific.
Another approach that may be worth looking into is can you get CHM outputs from those old projects. If so, you should be able to reverse engineer those. See Reverse Engineering on my site. Then you could generate webhelp.
See www.grainge.org for RoboHelp and Authoring tips
Thank you. I forgot to mention the most important thing--the help files I currently have are .hlp. Can these be imported into RoboHelp from ForeHelp?
As you have the HLP file you'd be better off creating a new project in RoboHelp. When you do this there is an option as part of the project creation to import a HLP file. As Peter explained you are likely to have some clean up though.
I'm hesitant about importing as I don't know ForeHelp. As long as you have HTML files you can import the files into RoboHelp but you probably have to recreate the TOC and index.
Once you have the help in RoboHelp, you can generate WebHelp for a client/server application. You may also want to look at the new Multiscreen HTML5 output as that is also very suited.