A point-blank shot is fired from very near its target, and a point-blank statement is blunt and straightforward. During an old-fashioned gun duel, people would settle an argument by shooting at each other point-blank.
The original meaning of point-blank, "close enough to hit the center of the target," definitely comes from French, although its origin is a bit of a mystery. Some think the source is point blanc, "white point," referring to the white circle in the middle of a target. Others believe it stems from de pointe en blanc, "point in empty space," used to describe a test shot fired into the air.