1. Does God have free will? Yes.
2. Are we made in His image? Yes.
Now, why would you attribute to man a free-will that God doesn't possess? In that, I mean, why would you think that man could possess a free-will to do that which he doesn't want to do, and which he is incapable of doing?
Can God sin? No, and He doesn't want to.
Can the unregenerate man please God? No, and he doesn't want to.
The unregenerate man is free to do exactly as he wants.
If God can't sin, whether He wants to or not is irrelevant.
I think it far more likely that sin is within God's capabilities, as is all else, but He chooses otherwise.