Lord of the Rings is very much about free will.
You are right. That is very much one of the major themes. The very purpose of the One Ring is to enslave the will of others. This is what Sauron does with the orcs—they can't help being loyal to him, because they lack even the will to do otherwise. This is the worst crime, the worst sin, in Tolkien's opinion. Tolkien was in favor of monarchy, but not in favor of tyranny. He hated the idea of dictatorships, even benevolent ones, maybe even
especially benevolent ones.
Which is why he said in one of his letters that if Gandalf claimed the Ring he would be
worse than Sauron. Why? Because with Sauron the line between good and evil still remains, if a little blurry at least still firm. But if Gandalf had the Ring and ruled the world, he would still work for good but under the corruption of the Ring he would
force everyone else to be good (as
he defined good) as well, he'd remove their ability to be anything else, to choose for themselves, thereby making "
good detestable." (Tolkien's own description of the result.)
But fortunately, the Ring only grants power according to the stature of the one who possesses it, and only in accordance with their nature (and to some extent the circumstances under which they obtained it—which is why Bilbo's mercy toward Gollum was so important). The Hobbits don't want power. They are an independent people. In the Shire they have the Mayor, the Thain, the Master of Buckland, all respected figures, but none with a huge amount of authority. So all the time that Bilbo and Frodo have the Ring, it never occurs to either of them to use it to wield power over others. Even Isildur, who was already a king at the time he took the Ring, in all the time he owned it he never turned evil or tyrannical; seemingly, it wasn't in his nature. And therefore it would have taken a much longer time to really corrupt him. (Despite what Peter Jackson's film implies.) No wonder the Ring "wanted" to return to Sauron, because all the time it belonged to Bilbo or Frodo, it couldn't fulfill the function that it was made for.
Tolkien's characters do believe in Fate, they do believe that Higher Powers may be at work. But those Higher Powers (Eru, and the Valar) only place people in certain situations, nudge them in certain directions, while leaving them free to make their own choices. So many of Tolkien's stories are tragedies (those who know only The Hobbit and LOTR often don't realize this) because characters make wrong choices, because they turn aside from the task that is clearly before them. The reason why LOTR ends happily, is because in a rare instance in the history of Middle Earth, enough people
do make the right choices. Frodo and Sam don't know that they make it safely across Mordor because Aragorn and his allies have created a distraction at the Black Gate. They only know their own tasks (Frodo to carry the Ring to the Cracks of Doom, and Sam to help him in every way possible), and that if they don't do what they set out to do, nobody else will or can. Aragorn doesn't know exactly where Frodo is, or whether he still has the Ring, or whether he is still true to his promise. These characters and others act simply on faith—that if they each do the task that is given them,
maybe things will work out.
Characters like Saruman and Denethor know what they are supposed to do, but for ambition (Saruman) or despair (Denethor)
choose to do otherwise, with fatal results. Yes, Sauron is manipulating them through the visions he shows them in the palantír, but they make their own choices.