Like you I use Windows 7, and can tell you instantly that some older Microsoft programs do not work with Win 7, whilst some other ones do. If you have Windows 7 Professional or Ultimate you can try running Frontpage in Administrator and Windows XP compatibility mode.
Windows 7 Professional and Ultimate instructions:
A. Right Click on the Program name if installed (Could also try with install too if not installed)
B. Click on 'Properties'
C. Select 'Compatibility Mode'
D. Try using the different 'Compatibility Modes'. I would try 'Windows XP Service Pack 1' first, if this does not work, try 'Windows 98'
E. Click 'Apply' then 'OK'
F. Right click on the program name that you selected compatibility mode for above, and select "Run as Administrator"
G. Follow any further instructions
If this does not work, then it will probably be cheaper to find a used newer version on a site like eBay. Note that Frontpage 2002 has Windows 7 issues too, so please check out the following links.
Good Luck
http://social.answers.microsoft.com/Forums/en-US/w7programs/thread/649f6c9a-4b7e-4557-b136-bf90b3b3c9e2
http://www.microsoft.com/windows/compatibility/windows-7/en-us/default.aspx
http://www.microsoft.com/windows/windows-7/compare/default.aspx