Finnegans Wake is many things. A mighty cathedral of academic speculation, interpolation, interpretation and derivation has grown up around it. Hell, it put Joseph Campbell's kids through college and gave Marshall McLuhan all his best jokes.
Just for fun, let's pretend it means what it says.
Finnegan is the universal mind — humanity's collective consciousness before we became collectively unconsciousness. That universal mind shattered into millions of pieces — the shards of separate identities who call themselves "I." The reason for the fall is fairly plain. The complexity of human civilization overloaded the collective mind's capacity. Cities, to be precise.
Collective humanity is dead/asleep. Like the Red King, Finnegan dreams. Those dreams are our individual lives. We're all guests at Finnegans Wake. And the last damn thing we want is for the guest of honor to wake up.
Finnegan dreams. It's a small cycle of dreams with a small cast of characters. We labor under the illusion that history is linear. It's actually a circle. Or a series of reruns. The same old story, over and over. A series of patterns which we mechanistically repeat — otherwise known as karma.
If you take that as metaphorical truth, you'd need at least a graduate level education before you could hope to discuss the matter intelligently.
If you take that as literal truth, it's an interesting SF premise. The first question being ...
What would it actually look like when Finnegan awakened?