Some extra context - Actually this battle was a bit more complicated. The Mongol army was accompanied by (but not allied with) some late Crusader Christian. The Crusaders stayed neutral and recognized Mongols as the greater threat than the Egyptian Mamluk Muslims.
They went back and forth on the Mongols. Remember that that the latter got as far west as Poland the Holy Roman Empire so it’s not like they hadn’t seen them up close. But they did romanticize the brutal Mongol derived warlord Timur or Tamerlane as something of an ally. Marlowe wrote plays about him.