You don't say what version of Fusion you are trying to run. It sounds like you have an older version of Fusion installed before you upgraded to macOS 11, and that is the version that is refusing to run after you upgraded macOS.
The solution already is available: Fusion 12. Fusion 12 supports Intel-based Macs running macOS 10.15 "Catalina" or later releases (and that includes macOS 11.x "Big Sur"). From what you're describing, you probably will need to upgrade. Your virtual machines should continue to run.
And no, versions of Fusion lower than 12 are not supported for macOS 11. There are lots of changes under the hood in macOS that required changes to Fusion - and those changes are not available in earlier releases.
If you're using Fusion for personal use, Fusion 12 Player is free and has equivalent functionality to the Fusion 11 "standard" non-pro version. If you're not using it for personal use, then you'll need to buy that license for Fusion 12 Player.
- Paul (Technogeezer)
Editor of the Unofficial Fusion Companion Guides
