Correction: When fighting a blinded guy, you only get a distinct advantage against him when you decide his blindness is narratively important (i.e. when you spend a Fate point). When it comes time for him to actually fight, the GM can and should compel that "Blinded" aspect liberally. Think Han Solo at the beginning of Return of the Jedi to see what a "Blinded" character looks like in a FATE fight scene.
The FATE step by step for Han Solo is...
Harrison Ford: "Boba Fett is right behind me, so I want to bat him with this staff thing."
Storyteller: "But you're blind. I'll give you a fate point if you don't attack."
Harrison Ford: "No, I really want to hit him. Here is a fate point to pay off the compel."
"Where is he?" *Turn, slap boba fett and send him flying with his jet pack*
Then later...
Harrison Ford: "I'm gonna use this blaster to try to shoot the tentacle."
Storyteller puts a fate point on the table: "I think you're gonna miss outright."
Harrison Ford: "Crap, I don't have any fate points left to pay this off. I guess I hate to miss." *collect fate point*