No, St. Augustine also taught we have free will.
For instance, St. Augustine teaches that some of those regenerated and justified in Christ are among the elect, but some are not.
We, then, call men elected, and Christ’s disciples, and God’s children, because they are to be so called whom, being regenerated, we see to live piously; but they are then truly what they are called if they shall abide in that on account of which they are so called. But if they have not perseverance,–that is, if they continue not in that which they have begun to be,–they are not truly called what they are called and are not; for they are not this in the sight of Him to whom it is known what they are going to be,–that is to say, from good men, bad men. (“On Rebuke and Grace” (De Correptione et Gratis), Ch 22)
… But those who do not belong to this number of the predestinated … [some] receive the grace of God, but they are only for a season, and do not persevere; they forsake and are forsaken. FOR BY THEIR FREE WILL, as they have not received the gift of perseverance, they are sent away by the righteous and hidden judgment of God (ibid, Ch. 42)
If, however, being already regenerate and justified, he relapses OF HIS OWN WILL of into an evil life, assuredly he cannot say, “I have not received,” because OF HIS OWN FREE CHOICE to evil he has lost the grace of God, that he had received. (ibid, ch 9)