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Even though it it said the Jesus didn't force Judas to betray Him, He did know that Judas would.
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Thus the paradox of free will and predestination.

C.S. Lewis discusses this (in "Mere Christianity" I think).
Basically he says that Jesus (and God) can see into the future, since they are "outside of time."
If that's true, then no paradox - as you said, you have free will AND Jesus/God know how you are going to choose.

It's more complicated than that. If God were an independent observer who had nothing to do with the creation of the Universe, then I could see that being outside of time He would just be watching the life of the Universe spin out like a movie where he could see all of the scenes instantaneously.

But He did create the Universe and so He had something to do with how we ended up. If the Calvinists are right, then He decided ahead of time who would end up in Heaven regardless of their free will. But I've noticed that people tend to be in one of two camps: they have more universalist beliefs and think that most people are going to eventually end up in Heaven which seems too merciful, or people tend to believe that their particular set of beliefs is imperative for salvation and so very few end up in Heaven which seems too unjust.

The general response is to state that God's knowledge/mercy/justice is so far above our understanding that we shouldn't try to explain it. We should just hope and pray that God will give us the grace to be saved. That seems a bit too antinomian to me.

And by "antinomian" I don't mean the normal definition that we are above the Mosaic law or law in general. There is a rarer usage which says that God's Law is so above what forms of laws we have on Earth that it is impossible for us to understand His mercy or justice.

This is one of the answers to the Problem of Evil, i.e. that no matter what horrendous and seemingly unmerciful and unjust atrocity is visited upon a person there is a good reason that God allowed that to happen.