I would say that free will interacts with fate to initiate the curse. There are free choices made by Laius, Jocasta and Oedipus that result in the fulfilling the curse's promise.
When Laius and Jocasta find out from an oracle of Apollo that their newborn son will one day kill his father, they abandon the child, leaving him in the elements to die. However, a kind shepherd takes the child and gives him to the King of Corinth.
Fate does rule but it is also put in motion by the actions of the human characters. Had Jocasta and Laius not abandoned the child, then Oedipus would have known who his father was, they thought they had solved their problem by leaving the baby to die. So technically, their actions set the curse in motion.
Technically it is freewill that really instigates the process of Oedipus not knowing who his father really is, Laius, and as a result of his bad temper and his father's bad temper, they fight on the road and Oedipus kills Laius over a silly argument.
Again free will plays a role in engaging the curse. Had Oedipus not gotten so angry at the older man for striking him, he would not have killed him. But the nature of the two men, Laius and Oedipus resulted in a heated argument that ended with the fatal blow from Oedipus to his father.
Sophocles writes this story to illustrate a fatal flaw in the human character, pride.