The story of Jonah does not contradict the idea of free-will. It is very clear that Jonah’s will was that he did not want to go to Nineveh.
It is clear that he took proactive decisions to not go to Nineveh.
The rest of the story tells the negotiations between God and Jonah to get him to Nineveh. Simply because the outcome is that God’s will rather than Jonah’s was accomplished, doesn’t mean that Jonah was a mindless robot.
A parent can make a child do his will against the will of the child. This does not mean that the child has no free will. Free will is not the ability to do what you want, but the ability to take action to attempt to do what you want. It is the ability to resist instinctive responses.
Ultimately Jonah chose to go to Nineveh. It was a conscious act at that point.
Christ wrestled with his own flesh which instinctively desired to preserve itself, against his purpose to face the cross. In the flesh he did not wish to die, He made a conscious choice to die on the cross. This is the meaning of the bruised heel of the seed of the woman and Jacob’s withered thigh.
We were predestined to have a choice.