By God preventing Bilaam from cursing the Jews, was that not an impingement of Bilaams free will?
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Bilaam had free will - but he also had a heightened awareness of Gcd's presence.
As a prophet he was acutely aware of Gcd's ability to punish; and he even got a "refresher course" on his journey, in the episode with his talking donkey.
Compare it to this: You find a perfect spot to park - but it's there's a no-parking sign and a policeman standing nearby. Would you consider that an impingement of your free will?
Of course not! You are simply in a situation with a heightened awareness of the law's ability to punish you.
Both you and Bilaam have the physical ability to do whatever they please - park or curse - so you have free will. But you both realize the consequences of making the wrong choice.
See this Q&A for a similar idea with Paro's free will.