Just before closing time the previous day, a 28-year-old woman scrawled the 30cm (12in) graffito on the bottom of the painting and was immediately detained by a museum guard, France's 20 Minutes news website reported.
Mr Wright later uploaded a picture to Twitter which showed five or six words on the bottom-right corner of the painting with black streaks of paint running down from the daubed writing.
Geary is on the right side of the painting under the White Star flag, amid his troops, who stretch from the bottom of the canvas and up the right side.