God created man and woman in Genesis 1, and gave them a command to obey (Genesis 2:17). However, we see that Adam and Eve disobeyed God (Genesis 3:6). To this extent Adam and Eve were certainly able to make a choice. When Adam and Eve chose to eat the fruit from that tree, they experienced the consequences of their actions, justly assuming personal responsibility.
However, after Adam and Eve’s sin all humanity has been corrupted (Psalm 51:5; Romans 5:19 ), that is, we have what the Bible calls a sinful nature (see e.g. Romans 7:18 NIV). What this means is that the desire of our hearts is naturally set against God and his ways. As Genesis 6:5 says: “The LORD saw how great man’s wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time.”
We’re now in a position where we can consider whether humanity now has “free will” or not, and if we do what that “free will” might be like.
Given Genesis 6:5, humanity clearly doesn’t have absolute free will – since the desires of our hearts are towards evil. This means that I cannot choose of myself, to do what is pleasing to God. It means, ultimately, that I cannot “choose” to become a Christian (this is why the Bible describes non-Christians as slaves (John 8:34), and as dead (Eph 2:1-3) – because of ourselves we are all hopeless and helpless).
This gets us to the heart of the gospel where God gives new birth to us as a free gift (see e.g. John 3:3-8; Eph 2:5, 7-10; Col 2:13-14). Salvation must be a gift to us, because we are all naturally enslaved and dead (and slaves cannot free themselves; and dead people can’t make themselves alive).
So in this sense, no we don’t have free will: we walk in darkness, because our deeds are evil (John 3:19). We cannot choose to please God or to follow him – we are not “free.”
However, we do have freedom to act according to our nature. As has already been said, for the non-Christian, their nature is sinful. This means that the non-Christian acts according to this nature – everything that they do is against God: even the best, most kind, or loving deed they do to other humans is, from God’s perspective, evil (Gen 6:5). However, non-Christians can “freely” act according to this nature.
Similarly, with Christians – we too act according to our nature. Yes, God has given us a new nature in Christ (2 Cor 5:17), but the old sinful nature still dwells in us. Therefore, our needs now tend to be mixed; sometimes we act according to our new nature and do what is good and pleasing to God, but at other times we still sin. This is Paul’s tension in Romans 7:13-25.
Scripture testifies to man’s responsibility and freedom and yet, also testifies to God working all things together, holding all things together, allowing and ensuring that all things come to pass or not come to pass (See Genesis 50:20; the various prophecies in the Old Testament; Romans 8:28-29; Romans 11:36; Colossians 1:16-17). Our freedom is act within our nature is within the cosmic system that God superintends: we experience freedom to make decisions and execute actions, and yet God knew about our decisions before the beginning of time, and allowed us to make our decisions – whether the decisions be for good or evil (Proverbs 16:4). Our freedom to act according to our nature does no violence to God’s sovereign decrees and God’s decrees do no violence to our freedom of will. God is God and we are to trust that He has the absolute and incomprehensible ability to create a world in which everything is pre-ordained while still giving humanity responsibility.