If the Bible says the unbeliever is not "free" then he is not free. The Bible says the unbeliever is deceitful and sick (Jer. 17:9), full of evil (Mk 7:21-23), loves darkness rather than light (John 3:19), does not understand, does not seek for God (Rom. 3:10-12), is dead in his trespasses and sins (Eph. 2:1), is by nature a child of wrath (Eph. 2:3), cannot understand spiritual things (1 Cor. 2:14). How then is the unbeliever able to choose God? He cannot.
This makes God responsible for evil
God is not responsible for the evil that is accomplished by the free will actions of fallen people. Remember, free will is the ability to make choices and unbelievers make choices consistent with their fallen natures. They openly choose to accomplish evil deeds in contradiction to God's Word. They are openly and freely rebelling against God. God did not make them sinful. He did not make them rebellious. therefore, God is not responsible for the evil but they accomplish it.
God made Adam who was good. Adam was not bound by its sinful nature and freely chose to rebel against God. Because of his rebellion, he fell. His body was physically affected by sin. Likewise, his children inherited the sinful nature and depravity of mind, soul, art, body, motions, etc. and are under the proclaimed revelation of God concerning their fallen state. Nevertheless, God made Adam good and Adam chose to rebel. We inherited the sinful nature and the unbeliever, the unregenerate can only act in accordance with his own fall in nature. In other words, he cannot choose to freely follow God because that is a good thing to do. Since he is a slave of sin, does not seek for God and does not understand spiritual things, he is not able to freely choose God.