On the show, the Siege of Paris occurs in the year 804. However, Paris was actually first attacked 41 years later and the year-long Siege of Paris did not actually occur until 885.
The Crossbow, while invented by the Chinese BCE and used by Ancient Greeks and Romans, didn't appear in medieval Europe until the 10th century.
The Priest who gives Gisla the banner for Saint-Denis is wearing a white habit. Saint-Denis is home to a Benedictine Abbey. Benedictine monks don't wear white habits. Rather, the Cistercians and Trappists do and are both followers of the Benedictine Rule of monasticism. However, the Cistercians weren't founded until the year 1098 and the Trappists until 1664. Benedictines wear brown.