Ok, got it.
Here is what I have found out, just in case someone runs into the same problems:
1. The FME integrated in MAME is NOT MFME, it is M.A.G.E.. Sometimes also called AGEMAME or MAMEA.
2. There are other emulators like BFMulator, JPeMu and Project Amber, but
3. The one to use is MFME.
So I found MFME on various websites in multiple versions. The newest version seemed either 9.4 or 10.1 from 2010 as they obviously had the highest version numbers.
But, what can I say, the newest version is 5.1 and it is even from 2017. Use that version and you are happy. It seems to emulate just everything fruit related and has even scaling support.
So MFME 5.1 with Trouty's collections (as Connie said, you need ROMs, Layouts and optionally Snapshots) is (imho) the best combination for FME.