bridge是先行词,off which they both fall into the river修饰它
off 是必须的,they both fall (into the river) off a bridge
fall 是不及物动词,后面必须接介词,定语从句中介词提前到关系代词前
句子拆分：
A poem line describes a fight
a fight between a Turkish and a Bulgarian officer on a birdge
they both fall into the river off a bridge