Reddit reviews Hero System 6th Edition Basic

The following are great dark medieval games, but some might require you to remove their magic systems:

• Aquelarre, IMO the medieval RPG, but to play it now you have to read Spanish for the original version. An English version is coming this year.
  
• Cthulhu Dark Ages, where the players most likely wouldn’t have magic anyway
  
• Rolemaster Classic. You will need Character Law and Arms Law. There is a Spell Law book, but without it the world has no magic.
  
  Other than that I would recommend generic systems like GURPS, Hero System or Genesys.
  
  Some would recommend Fate also, but I generally think it is rules-light but adventure-crunchy, since you have to remember during play many contextual situational modifiers with the aspects' system. Instead, I would get its parent game, Fudge. You need special dice for this, and for Genesys also.
  
  Some of the editions I linked above are older than the most recent, and reflect personal preferences.
  
  Other systems, although great in itself, really work best when you have at least the effects of dark corruption like Zweihänder.

GURPS Lite is strictly d6, and a nice generic system for most basic needs, and free for download. You can upgrade if they like it and it's on it's way to proving that it is infinitely extensible.

I'm also pretty pleased with the Hero System Basic Rules book as generic systems go that are d6 specific.

Traveller is also d6 only, and a really nice generic science fiction system. Totally playable from the core rules, but also infinitely extensible.