Yes, salvation is indeed a free gift of God. The fact that we need to submit our intellect to Him in an act of faith does not mean that we have earned it by this act. In the same way, because we also need to submit our will to him in an act of love also does not mean that we have earned it by this act. In both cases we are merely accepting the free gift of God. The good works that must accompany our faith are the product of our will, our love of God. Faith, the intellectual assent to God, is not enough.