If you mean the help browser that you get in SolidWorks 2010 when you use the help buttons or F1 from within the interface and have the Web Help turned on, this is a custom browser that is based on Internet Explorer. You cannot set it up to use Firefox. We used a custom browser so that there could be communication between SolidWorks and the browser. If we used a standard browser, then every time you hit a help button or press F1, a new browser window/tab would open (depending on how you have your browser settings) since SolidWorks would not know to which window to target the results. With a custom browser, we can always target the results to that window. The custom browser internally uses whatever version of Internet Explorer is installed on the machine (we support Internet Explorer 7 or above - the results with Internet Explorer 6 are very poor).
That being said, you can use Firefox to search and browse the help independently from SolidWorks by going to the URL help.solidworks.com. As stated, using help buttons and F1 from within the application cannot "target" this window, but everything else should work the same.
I hope this helps,
My company uses Explorer exclusively for things like timecard info, etcetera. We're at version 6. I am not sure I can upgrade this to 7 because of compatibility issues with company apps that are based on IE 6.
I'll do the search outside of SW using the URL you suggested.