What version of Windows are you sing? Findfast was a utility in Win9X and as far as I'm aware was replaced with different technology in XP. Mainly because it was a PITA and used a lot of system resources
I'm casting back my memory now, but I think that Fastfind was ALSO installed when you installed older versions of Office, Microsoft trying to get in on the machine either way....
From the error message you are getting I assume you are running Version 7 of Avast. This has a problem with the sandbox technology in that Avast haven't "whitelisted" a lot of the old Microsoft programs. Office 2000 and Office XP are examples of genuine programs which throw this error.
My guess is that either
1) You have an old version of Windows (95/98/Me/2000)
or
2) An old version of Office (anything pre-2003)
or
3) You really do have a virus
If ether of the first two are correct, then allow the program to run normally - but my advice is to then disable it. The performance hit it creates isn't worth the gain
Disabling it is a two part thing - you have to stop the service and then delete the indexes. Just how depends on the version of Windows - and I'd need to refresh my memory from the resource kits before advising more