Yes, anyone without a criminal background is eligible to have a FFL, though the license holder will have to conform to state, and local law. Which in some state for example Massachusetts means the FFL holder must have a store front separate from a residential building (no operating out of ones home), must have a state business license, filing as a business for tax purposes, and collecting sales tax etc. Pain in the ass to have an FFL in this state. C&R licenses are not regulated under state statures.