Yes, we do have free will, and here's why
There are very many who have written wise words about free will who are far more knowledgeable than I, but there is one point about free will that I think can be easily explained and that could clear up what I believe is a major misunderstanding. It's to do with who and what gets to make choices.
Free will is an odd thing, as it's not what most people seem to think it is, because what most people seem to think it is turns out to be impossible. The most common idea of free will is that it is control over reality that is not somehow limited by physical laws: there is some sort of thing that is the self that can have will, and can choose how to exert that will in a way that is not predictable by science. Our self and will somehow step outside of physical reality and so we can think what we want to in a way that is not determined.
That makes no sense, because what we think has to be determined otherwise it is just arbitrary. Given a certain series of facts (including our mood and feelings) to make a decision about, if we don't make the same decision given the same situation then our decision is arbitrary. That's not really free will, is it?
What we want with respect to free will is that it is us making the decision. But for it to us us making the decision, then there has to be determinism of some kind. The alternative to determinism is not freedom, but unpredictability.
So determinism is not the enemy of free will, it's necessary for it. This seems utterly counter-intuitive, but it's the wrong way to look at things. Determinism is not a prison that forces our choices, it's a framework that enables us to make choices. Freedom is not destroyed by predictability.
What really matters for free will is who or what gets to make choices. To understand that we need to understand what we are. We are humans. Each of us has a body, and a brain, and the activity of the latter results in our minds. We don't normally attribute choice-making to our bodies as a whole. We don't talk of our hearts choosing to beat, for example. What we tend to think of as having the power of choice is some vague combination of our minds and brains.
I believe that we can think of free will as what happens when what has the most influence on what happens is activity in our brains that is more or less associated with our minds. It's when that is the location of the "switch" between outcomes. It doesn't matter if which outcome happens is ultimately determined by physics, what matters is that it's the physics of thought in our heads - if it's the physics of "us". It's our will because we are where it happens, and it's free because we are the place where the choice is made.
Another way to look at this is that in a deterministic universes there are vast numbers of causal links. Our will is free when the most significant causal links involved in determining what happens go through our brains.
Free will is when we are where the causes happen, even if the causes are predictable.
This is in contrast to the situation with a supernatural reality. There is no clear indication of causality with supernaturalism, and here is the possibility of reality being constrained by other beings, such as gods who have "a Plan". Contrary to the suggestions of religions. It's supernaturalistic theism that makes freedom questionable, that removes our powers to act, to have moral choices and responsibilities.