From Apple’s web site:
Final Cut Pro 4 and earlier versions are not supported on Mac OS X 10.5 Leopard.
While the current version of FC is 6, many videographers stick with older versions for the basic reason of "If it ain’t broke, don’t fix it".
If you upgraded to OS X 10.5 and wanted to continue using version 4, you’re out of luck and will have to upgrade or buy new, which will run you up to $1,300.
If you want to know if your current older Mac meets system requirements for Final Cut Studio 2, the product page for FCS2 will give you the scoop.

That’s so unfortunate that we the people have to find out “after the fact.” I just did a clean install of Leopard on my 2003 Mac Powerbook G4 with no problems until I wanted to reinstall Final Cut Pro 4. It installed but got caught in the loading of Audio files on launch of the program. I think I will go by iLife with imovie and just use it. I may take Leopard off and go back to Panther where everything worked fine, then upgrade to Tiger.
Annie, I understand your frustration. I just upgraded to Tiger and now my Final Cut 4 will not capture cleanly so you might try a different alternative. I’m contemplating going back to Panther as upgrading FCP is so costly.
John