He fell over和 He fell down 都可以
fall over:强调的是“向前摔倒、跌倒”.
She fell over and broke her leg. 她跌倒并把腿摔断了.
fall down强调的是“滑倒、倒下”,后接宾语时应加上介词from
If people run across the road,they may fall down.
如果人们跑过马路的话,他们可能会摔倒.