The three biggest reasons...
A - Admittedly less interesting than the next two, but Finn is pretty decent with a LS with zero experience. He is also exceptional with other weapons the first time he tries them. He did have extensive training with what passes for conventional infantry weapons as a storm trooper though.
B - Finn reacts to the death of planets/entire populations. When Starkiller Base destroyed the Republic planets Finn knows. We've seen that before, and it was from one of the most powerful Force users in the movies (Kenobi).
C - When Snoke asked Ren if he also felt the "Awakening" we have still not seen any of Rey's incredible Force feats yet, but Finn had done several impressive things.
Rey is special, even among Jedi/potential Jedi (heck, even the Skywalkers would be impressed with the things she does without training). I think Finn is more garden variety Force Sensitive.
That's not an extensive list of hints either. He breaks the storm trooper conditioning program (the one that makes them fanatically loyal), he survives the open desert, Kylo Ren senses something powerful change in Finn (I think perhaps his "Awakening") and stops what he's doing and notices, and he remembers him later from that one short moment.
