The fact that other than our fear of it, “everything (else) is in the hands of Heaven” does indeed bolster Rambam’s argument for our free will. But let’s first explain just what the fear of Heaven is all about.
First off, at a certain point in his writings Rambam proclaimed that fearing G-d “leads to wisdom” and that it’s “even more precious than it”, which is a phenomenally significant statement on his part, considering how much he valued wisdom.
But as to how we can cultivate this important trait, he disclosed elsewhere that we come to learn how to fear G-d by “fulfilling His mitzvot”, which is to say by subjugating ourselves to His will and wishes. In fact, the Torah itself links the fear of G-d to the performance of mitzvot, as well as to free will, when it says in G-d’s name, “O, that there was such a heart in them always! That they would fear Me (on their own) and observe all My mitzvot” (Deuteronomy 5:26).
But Rambam gets more specific about it somewhere else. He belittles the sort of simple, better said, primitive sort of fear of G-d that the less- sophisticated of us (whom he calls “ignoramuses”) sometimes exhibit: the sort of emotion that leads them to be observant in order to avoid calamity or Divine retribution, or to dwell in Heaven after they pass on. He contends that doing that belittles the worship of G-d.
The sort of fear of Heaven he advocates at yet another point is the one a person comes to when he or she “contemplates the great wonders of G-d’s handiworks and creations, and sees that they are the product of a (degree of) wisdom that is boundless and limitless”, and he or she comes to “feel a great sense of awe and trepidation”, and to realize “that he is a very humble and insignificant creation with barely a grain of intelligence compared to G-d”. That’s to say that Rambam encourages us to look upon things with G-d’s profound being in mind, and to stand dumbfounded in His presence.
The point, though, is that this is in our hands alone; G-d doesn’t grant us it. We’re expected to foster it on our own.
So, what our sages were referring to when they said that “everything is in the hands of Heaven but the fear of Heaven” is the fact that there are indeed certain things that a person has no control over — like “being tall or short, whether it will rain or be dry, whether the air will be foul or pure, and other such common occurrences” — but not his or her own actions. For we have utmost control of the latter, which is Rambam’s whole point.
As such, we’re expected to take responsibility for all of our actions, and to strive for spiritual excellence.