The natural man in sin does have free will. There is no doubt. However, he only has free will in the natural world. That is to say, he is free to choose what he will eat or wear, think or do. In a word, he has choices in this world. However, he is spiritually dead to please God or do God's will, outside of new birth in Christ (Ephesians 2:1,5). He is in bondage to his own sin, and that includes his will (Romans 6:20-22).
The natural man has not been born again through faith in our Lord Jesus Christ. He is free to make his choices in this world, but spiritually, his will is in the bondage of sin. Only Jesus Christ can make him free from the bondage of sin. Does he have free will? Yes and No. Yes in his daily choices of the natural world. No to spiritual things that please God.
The natural man is in the bondage of sin. He may drink as deeply from the cup of iniquity as he pleases. His heart is corrupt. His spirit is in rebellion against God. He has no desire for God. His bondage to sin means that he is not concerned about pleasing God, nor can he (Romans 3:10-11; 8:8).
Only the Holy Spirit can convince and enable man to come by faith to the Lord Jesus Christ (John 16:7-11). Then, and only then, he is free indeed (John 8:34-36). By the grace of God, his heart is changed, which includes his mind, will, and emotions. His will is free in Christ from the bondage of sin. He is free to do God's good will (Romans 12:2).