There's an interesting theory I heard recently that Snoke is actually Mace Windu, and that Finn might be his grandson.
Finn is probably Force sensitive, but not at the same level as Rey or Kylo. There is some evidence in the film that he might be. I dunno that I buy the Snoke as Mace Windu part of it, but it does seem somewhat possible if you really think about it. He'd be old and scarred, and saw the Republic fall and Empire both rise and fall, something Snoke claims to have witnessed himself. Snoke is stark white, but so are Palpatine and Vader. There are reasons for that of course, and in Palpatine's case it's at least partially due to his exposure to his own Force Lightning, the same thing that brought down Windu after he lost his hand and threw him from the window.
Both Lucas and Sam Jackson also agree that he probably didn't die from that fall. No Jedi has died from a fall from any distance in any of the movies and Mace was alive and conscious when he was thrown from the window. It seems more likely than not that he survived.
Plus it is interesting that Kylo doesn't outright kill Finn despite how pissed off and injured he was. He seemed to deliberately not kill him even after he takes a blow to the shoulder. That's odd considering he had just killed his own father and when you factor in the origin of that table of ashes.
I think that at the least, whether the Mace Windu theory is true or not, that Finn is more important than the Force Awakens lets on and probably has ties to either Snoke or someone very important in the First Order.