No, it just shows that QM isn't an entirely random process--which is a good thing because the universe doesn't appear to be random--it does not show that we are unable to freely chose one path over another. If you believe that QM, which (A) appears to be random at heart, is both, a (B) correct model of how things actually work, and that (C) the universe isn't entirely random, then it follows there (D) must be something which influences the decidedly non-random events we see in the macroscopic world.
Based on your previous statements it looks like you would agree with A, B, and C; you've stated A, by virtue of bringing up QM you've implied that you believe B to be (at least close enough to) true, and since you believe that everything is "lawful" you must also believe C to be true. At this point if you don't accept D as being true your beliefs appear to be inconsistent (specifically, I would expect, how can a random QM universe be lawful?).
It appears that it is possible for something to influence the macroscopic nature of the universe, to choose one outcome over another. So, if we don't have free will it is not because the universe disallows the possibility.
OK. That is a trivial statement, no different than saying the something is either "blue" or "not blue", and such statements don't carry any weight because they can be said of anything. If you want to incorporate a Law of the Excluded Middle statement into an argument you need to use it to demonstrate, e.g., that choosing either something or its negation leads to the same conclusion and therefore the something is immaterial to the argument.
I'll accept that, (E) "something causes a choice" implies (F) "the choice isn’t free”, but I don't see any reason to believe that ~E -> F.
I'm not defining anything, I'm trying to see the logic of your argument based solely on your statements. So far your logic is lacking because you are drawing unfounded conclusions. It doesn't matter that you start with a trivial tautological statement (a perfectly reasonable way to start, IMO), what matters is that you are jumping to a conclusion. Why does, `it is not the case that something causes a choice' imply that `the choice is not free'?