Hard to tell whether it's a real or fake. There were many similar Ford signs over the years. At one time, I believe, there was an Andy Rooney repro sign of the same size.
I have two similar signs to yours. I believe that mine are repros. The first sign is double sided, while the second is single sided.
Compare to yours for any differences. I'm no sign expert, but there are definately some differences between mine and your signs. First, look at the font. Second, the grommet positioning is different. Lastly, the size of the font is different. The words on your sign are more spread out, while on mine they're more compressed. I believe that you have the real deal.