This kind of thing is pretty common with these academic apps.
The Mac app is just a wrapper around the command-line tools, which are installed inside the app.
You can run it from the Terminal. Execute the following command:
export PATH=/Applications/FullProf4Mac.app/Contents/Resources/FullProf_Suite:$PATH
Then run the command:
tfp
to start the "toolbar". I'm unfamiliar with this app, so I assume the toolbar is all you need to get started.
You can add the above command to your shell startup scripts.
If you want to get the app working again, open the file /Applications/FullProf4Mac.app/Contents/Resources/FullProf4Mac.sh and change line 188 from:
set versionX11Str_curr to GetAppVersionStr(appNameX11)
to
set versionX11Str_curr to "2.8.1"
I strongly recommend using BBEdit (https://www.barebones.com/products/bbedit/) to edit any file like this. If you are familiar with the Terminal, you could use vim or your favourite Terminal editor.
Note that this is a "hack", not a "fix".