No, good DR,( I know, I know, who am I calling good!)Paul sinned against God, as he knew better. He chose to sin, killing men, women and children,telling himself that he was doing God's will, but he knew the ten commandments, he knew everything in the Hebrew bible. Now you really are blaming God for our sins.
As a Pharisee's Pharisee, he thought he was doing God's work. Remember, the Torah had strict penalties for worshiping false gods. He did not even realize he was sinning, he thought he was righteous by his deeds. (We've read the story, so of course we know better)
Only when his sin was exposed to his heart did he realize what he was doing. Calvinists will say that is the same way it works in all Christians.
Now, when you read the story of Paul's conversion, deep in your heart, do you think he really had a free will? God in heaven speaks directly to him, blinds him, and he is terrified! Right away he sees that he is a sinner.
Not convinced? What about Jonah? Don't do God's will and you get eaten by a great fish until you repent and agree to do what God says. No free will in that story.
Still don't buy into it? Reread the 6th chapter of Isaiah and look at the fear God will put into the prophet's heart someone's heart! When God exposes our sin thought the Holy Spirit, we are also undone and realize that God wants us!
His message is so compelling that we thirst after it, just like water on a hot day. If we reject either one we are dead! Drinking water is free will, but how many will turn it down walking through the desert? God's Word is water for our soul. We will not turn it down!