If you are mechanically inclined, the mechanism can be easily accessed. I looked at my FE2, and if it is similar, it looks like a 'C' clip holds the cover plate (rotating release plate) in place. I would think you could remove the C clip and gently lift the plate and look for debris/piece of film lodged in the mechanism. The rewind handle can be removed by simply using a piece of wood/plastic between the legs of the rewind fork to hold it in place and gently turning the rewind handle counterclockwise to access the plate and clip.

Since I used to be a watchmaker I am somewhat comfortable getting into cameras. Not being aware of your background/skills please consider the above information and proceed at your own risk. Good luck.