There's a difference between Jedi and a being strong in the force. Rey and Kylo are clearly strong in the force, but neither are Jedi.
Poe is very likely strong in the force - you don't get to be that good a pilot unless you have really good "intuition".
It's clear that anyone can handle a lightsaber, but usually it's restricted to the Jedi because to be able to hit blaster shots you have to have that precognition and the training.
Against another sword or melee user, though, it not much worse a weapon than any other melee weapon, and you needn't be a Jedi to be somewhat successful.
It's clear Finn isn't trained in swordplay, though, so while he's able to use it somewhat defensively, his continual pining for a blaster reflects his skills and preferred weapon.
But I doubt they are going to have him be a Jedi or strong force user, they need a contemporary to Rey to show off the difference and have two characters that can explain things to each other that the audience needs to know. If they both become the same thing that tool goes away.
Besides, they already had a high ranking black Jedi, so they've checked that political correctness box and don't need to turn Finn into someone extra special just to prove they aren't racist.
