Was Faulkner right? Do we have "a soul, a spirit capable of compassion and sacrifice and endurance" (etc.)? Many atheists resist that kind of talk, preferring to attribute our heroic virtues to intelligence and rationality and other evidently-evolved traits.
But I don't think a secular humanist should ever cede the language of spirit to the supernaturalists. Spirit means breath, soul means life. Breath and life require a natural host. Simplify, simplify. But don't oversimplify. We're not automata, we have feelings that enter inextricably into our thoughts and actions.
Most walkers step confidently in the conviction that our human essence is experienced most vitally in its native habitat, on planet earth, the only world we've ever known. The earth of things, objects, entities, relations, processes, and physics is our spirit's abode.
Jennifer Michael Hecht wrote, in The End of the Soul, that "for atheists the significance of life is greatly increased by the disappearance of an afterlife: the absence of an eternal life allows mortal life to bloom in importance." And when mortal life blooms, spirit breathes free.
This is that delightful old "vision of life at once spiritual and deeply rooted in 'the open air and possibilities of nature'" that I caught from William James a long time ago, a vision that "assigns a destiny-shaping, evolutionary role to the emergent personal and cultural forces of intelligence and the human spirit as gifts of nature... that finds nothing incongruous about nature and spirit in harness together."
And in one of James's more clever turns of phrase and table: "the conception of spirit, as we mortals hitherto have framed it, it itself too gross to cover the exquisite tenuity of nature's facts." Human spirituality naturalized is more subtle and sophisticated than anything ever cooked up in the traditional religious philosophy shop.
So, the end of that soul is only the beginning. Take a breath, and take another step. Whatever Faulkner meant, godless humanists are entitled to invoke the spirit.