I'm only marginally familiar with Frostpunk as a genre - what sort of game is your friend looking for? Gritty apocalyptic survival with some settlement building aspects?
Are you looking for a somewhat generic system that can handle a Frostpunk genre game? If so, Cypher System, Savage Worlds, Cortex Prime, or Fate would work depending on your other preferences in a system style.
I was trying to recall a TTRPG that I saw a while back that specifically focused on building a community that would work, but I'll have to post it later when I figure it out. Stupid faulty human memory.
It really depends what kind of game you want to play.
If you want a fiction first game where the characters are a bunch of "freedom fighters" in an hostile environment, you could try either Spire or a|state, but you would need to heavily modify the settings. It would be a lot easier with a|state, which is a dystopian future hack of blades in the dark.