He doesn’t appear in RDR 2, though his gravestone might. His gravestone definitely appears in RDR 1.

As for how he died, we don’t really know. His epitaph reads “Always took a joke too far”, suggesting that this led to his death. Taking his age into account as well, we can deduce that he was likely shot and killed, possibly relating to taking a joke or prank too far.

I was thinking about that random encounter where the guy shows off his new gun to his friend and accidentally shoots him? Maybe it could relate to him?

I don’t think Francis Moon would necessarily have been killed that way, but it’s roughly in the right direction of his death’s circumstances.

You just walked the pla- Francis? Dude? Wake up!-Herbert Moon, 1897