Fate could not operate without that choice, which is part of the web of fate itself, part of its colour.
Did not Odysseus reach Ithaka as he was fated to do all along? And did not that arrival require strenuous efforts and choices, the choice to leave the nymph Calypso for example?
To say that determinism and free will contradict each other is to confuse two things on very different scales.
The sense of choice, of decision and effort, are woven into the very fabric of fate. Free will is necessary for fate to unfold as it must.