Finn being force sensitive is kind of a weird thing to answer as we don't really have an answer to how even the Empire did it in the new canon and we know they did at least something with Force sensitives outside of the Inquistors. In legends they had units for Force sensitive cadets but that mostly went into special units like the prototype Saber guards and the few in number Shadow Guard (Shadow Guard being a thing Disney is Marketing so they may make a comeback).

Best guess if Finn was is that he was too small in power to be considered a threat, Finn was more skilled in other tasks as I'm pretty sure his first mission was Jakku, or it happened to be overlooked by people looking for it. Whats more is that I don't think the First Order has many variants in troops as they seem more concerned with successful basics before they branch out. It seems like the FO detachments are very small by comparison compared to the Empire so it may lack backing for one reason or another.