From the For-What-It’s-Worth Department.

Dictionary of Word Origins, Jordan Almond, agrees with the explanation that point blank is from the French for aiming at the white center of a target. Similarly, Etymological Dictionary of the English Language, WW Skeat.

Origins A Short Etymological Dictionary of Modern English, Eric Partridge, agrees (sort of) with the French derivation of point blank:

{tracing the many descendants of the root pungere, to prick.} 8. L punctum, a point, a dot, becomes OF-F point, adopted by ME; in several senses, E point (n) prob derives rather from F pointe, from L puncta, prop the f of the pp punctus. “To point”, ME pointen, comes from MF-F pointer, from the OF n point. The adj point blank derives from the adv, itself perh from F de pointe en blanc, from a point into the white (of the target); point-device or -devise, from ME at point devis, at point exact, OF-MF devis, exact, fixed, from L diuisus, (sharply) divided.

Pungere has a surprising number of descendants, including TEd’s cousin, pun.