[Mostly just writing this here so I don't lose track of the thought. But I'd love comments.]
According to Christianity, God is sovereign, i.e., controls all things. He is omniscient and has an all-encompassing plan which is guaranteed to come to pass. Thus, everything has been predetermined--or, to use the theological-sounding term, preordained.
Meanwhile, Christianity also claims that humans have free will (at the very least in the sense that they deserve to be held accountable for their actions, i.e., the choices a person makes over the course of their finite life here determine their eternal fate). Their choices are real, and they matter. Humans are agents. However, God's control of everything has to also include control of the fate/choices of each of these supposed free agents. How do we resolve this paradox?
A pertinent idea is that because God created the universe, He exists outside of it (though of course another central idea in Christianity is that He interacts with the universe and intervenes in its events). Humans, meanwhile, exist and act within the system of the universe. So when we speak of human actions, we are talking on a different level than when we speak of God's actions. The frame of reference is different.
From these premises, here is one way to consider human free will and divine sovereignty compatible: We can say that from outside the system (i.e., on the level of God's actions), everything within the system is deterministic because God set up the system, has a plan, and cannot be thwarted. With respect to God's will, everything within the universe is fixed. But at the same time, we can say that from inside the system (i.e., on the level of human actions), humans are agents, and their choices count as free because their choices are free within the universe--free if you don't look outside the system to God's plan. When they make choices, they don't know at the time which way God has predetermined things will go.
In sum, this interpretation says that subjectively, or relatively, we have free will. But absolutely, when we compare ourselves to God, we don't really.
(Note: A major source of confusion is that God operates on many levels. I only distinguished here between within the universe and outside the universe, but I'm sure there are many more levels at which God exists, since He is incomprehensibly and indescribably great.)
The more I think about this, the less sure I feel that this is a theologically sound interpretation. If our free will is really relative, how can we say that it is free in the first place? What if we try to resolve the paradox by saying that God has the power to control our every choice, but doesn't actually use it? But then again, given the premise God's plan is ineffable, undeniable, irrefutable, invincible, etc., all things ultimately have a predetermined outcome, so our free choices, even if they exist on an absolute level somehow, can't change the final course of events, in which case they can't have been absolutely free anyway...