Alatar explained things pretty well.
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You say that there is free will because they can choose the path they go down
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Yes.
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but then you say that Eru can tweak their souls to make them go down a certain path
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Yes.
Let me explain.
First, everyone must have a certain nature. How Eru decides what nature to give someone I don't know (perhaps it's mostly random?), but in certain situations it seems that He adds a little something to someone's nature to ensure that they are more likely to take a certain path.
Also, keep in mind that Eru can see what path their particular nature will lead them down no matter what nature they have.
So it doesn't matter if someone is fated to do a great task or not- Eru can already see the choices they will make. Therefore someone who was "fated" to do a great task was not given any less free will than the guy living next door to him who never did anything. They both had a certain personality and Eru could forsee exactly what their personality and circumstances would lead them to do.
I don't believe that knowing what someone is going to do ahead of time means that the person does not have free will to choose.