No, God doesn’t give people free will if you take it to mean that they can choose anything they want. I would define free will as this: every human being has the freedom to choose whatever sin he wants. That’s free will. You can choose whatever sin you want to choose, you just can’t choose not to sin.
So yes, there’s free will, but there’s only free will within the framework of depravity and corruption. The one thing you can choose is to get out of there. For that, you have to cry for the mercy and grace of God to extract you, which God does by His own sovereign love and power.
Sinners think they have free will, but the Bible defines sinners as being in bondage to sin. It is a bondage to sin so profound that the only thing they can choose is which sin to commit.