"He gave me a hard look."
Translation:Il m'a jeté un regard dur.
"Il m'a donné un regard dur" is not clear. What I understand is that "il" would be something, not someone.
Ex: "ce maquillage / la colère me donnait un regard dur" (make-up/anger)
If I want to mean that someone gave me a hard look, I would say: "il m'a jetté (or "lancé") un regard dur".