We should definitely remember to discuss the role of Men in the fulfillment of the Divine Plan (the one in Tolkien's fictional universe, of course).
So as not to exclude anyone who has not read the Silmarillion, I'll start by saying that it starts with a creation story. The god Eru Iluvatar and some divine assistants ('the Ainur') make The Music. This performs the world into existence -- not only its beginning, but much of how things will unfold in the future. The performance of The Music does not go without a hitch, however. One of the assistants, Melkor, adds his own ideas. These disrupt the performance, and result in a world that (an inhabitant of Middle-earth can't help but notice) contains chaos, strife, cruelty and other defects. Rather than attempt to correct this directly, Eru Iluvatar makes a further creation - the Children of Iluvatar (a.k.a the elves and Men). These creatures have the task of helping to heal the world. Of these two kinds of 'Children', Men have a specific and unique power (Tolkien calls it 'virtue', using an old sense of that word) with which to do this work:
“Therefore he willed that the hearts of Men should seek beyond the world and should find no rest therein; but they should have a virtue to shape their life, amid the powers and chances of the world, beyond the Music of the Ainur, which is as fate to all things else; and of their operation everything should be, in form and deed, completed, and the world fulfilled unto the last and smallest.”
Silmarillion Ch 1 - Of the Beginning Of Days (my italics)
What this gives Tolkien in Lord of the Rings is a fictional world in which fate and free will are two forces shaping events in different ways. However, it seems from the above that free will is exclusively Mannish .
Tolkien and his LOTR characters do not spend a lot of time trying to work out what is fate and what is free will. For one thing, I doubt lots of philosophising would improve the stories, and for another it's probably hard for characters to tell. But I think to would be difficult not to see both fate and free will swirling around the Bagginses, and the Choices of Master Samwise (So 'Men' must include hobbits for this purpose, for all the derision I expect you'd get for suggesting to a Hobbiton Inn that hobbits are Men).
And here's an Aragorn example -- after the funeral of Boromir, where Aragorn is working out whether to try to catch up with Frodo and Sam, or to rescue Merry and Pippin.:
“‘Let me think!’ said Aragorn. ‘And now may I make a right choice, and change the evil fate of this unhappy day!’
TT _ The Departure of Boromir
I think he means what he says literally. Everything has been going wrong that day, with the feeling of Powers At Work. But Aragorn's taking seriously the possibility that his next choice will be both free and fate-busting. Therefore he stops, considers carefully and hopes, or wishes (or, if you prefer, prays) that he will choose wisely, and make a choice that disrupts their current evil fate.
(I should say that of course I am nowhere near clever enough to have thought up all this by myself. I'm reflecting on what I learned in Prof. Verlyn Flieger's essay
The Music and the Task: Fate and Free Will in Middle-earth, from her book
Green Suns and Faerie, Essays on Tolkien.)