There are two version of how this term came about; we leave it to you to decide which to believe.

The archery version: The French verb point means "to aim," and the center of an archery target was once a small white spot, referred to in French by the word blanc, meaning "white." Hence "point blanc" meant "to aim for the white."

The shooting version: The term comes from sport shooting, where "point blank" was a term used to denote the first part of the trajectory, which was supposed to be a straight line. Later the point-blank range was that distance from the gun to the first graze of the shot on the horizontal plane when the axis of the gun was placed horizontal; this depended on the height of the gun above the ground plane, but it was the only method of determining the relative power of these early guns.