Correctly wiring GFCI with two hot lines
Pick a circuit and stick with it

It appears that the existing wiring is confused, as it so often is in buildings of such vintage, and as a result you have one receptacle device that somehow got fed two circuits (one always hot and one switched hot) in a way that probably simply rendered the switch useless (as it was backfed power from the always-hot circuit to its load side).

Your well-intentioned-but-naive GFCI hookup attempt failed because the GFCI was seeing at least some voltage on its LOAD side and tripping/refusing to reset as a way of signaling "hey, dude, I've been wired wrong and can't help you because of it!"  This is a very important safety feature in the current generation of GFCI receptacles -- instead of silently offering an illusion of protection, they will do everything but scream to tell you about outside power appearing at their LOAD terminals, as that backfeeding both can render the GFCI unable to provide protection and can damage the GFCI's internals.

So, you need to decide whether you want the GFCI on the always-hot circuit or the switched circuit, and cap off the wires in the box for the other circuit with wire nuts, then connect the wires on the circuit you want to use to the GFCI.  Just make sure to keep which hot goes with which neutral straight to avoid a giant loop in your wiring.