Nothing about free will suggests that it requires something outside of our brains.
It doesn't say there is something beyond our physical brains and everything physical they interact with.
Even physical processes are only superficially deterministic - quantum particles don't all line up neatly by themselves, you know.
If the brain is "nothing more" than particles going in trajectories obeying the laws of physics, I don't see where this "free will" thing fits in.
As for the "uncertainty" of quantum processes, first, from what I've read at least, most scientists posit that they don't really affect our brain processes, happening in sub-atomic scales and all, and second, even if some "randomness" exists, again I don't see how that makes it "free will". Quoting Harris here:
And to the extent that the law of cause and effect is subject to indeterminism—quantum or otherwise—we can take no credit for what happens.