The last version of Fusion 12 (12.2.5) would accept a Fusion 13 license key. Unfortunately that version won't run on Catalina. To run on Catalina you need 12.1.x which does not accept the Fusion 13 license.

If you have a paid Fusion Pro 13 or Player 13 license, you can log into your VMware account and downgrade it at the Customer Connect licensing portal. 

However, a personal use license can't be downgraded. You'll need to use the following site to register for a Fusion 12 personal use license (it's not the same as the site you used to register for the Fusion 13 personal use license):

https://customerconnect.vmware.com/en/evalcenter?p=fusion-player-personal