There are possible hints that Finn is Force-sensitive, but they are extermely weak:
Maz Kanata DID give him the lightsaber, for some reason. Instead of Han or Chewie (Shucks! I wanna see the Walking Carpet with a lightsaber!)
Finn has WAY WAY too much luck on his side, all the way through. Only Jedi tend to be so lucky.
He meets Poe (who's instrumental in killing Starkiller base in his X-Wing). He meets Rey and BB-8. He decides to return to the Resistance instead of running off with pirates, bringing his knowledge of Starkiller to them. He runs into Captain Phasma and her magical base shield passowrds just when needed.
Though, the experts seem to disagree on that point:
In my experience, there's no such thing as luck - Obi-Wan Kenobi
There seem to be way too many Force-enabled opponents if you count Snoke, Ren, and Knights, for just Rey to fight. Of course we can always predict a full stealing parallelization of plot from original Trilogy, with Ren turning "light" and offing Snoke in a fit of valiant last second teenage emo outburst.