The meaning would change in a way that made the sentence a little nonsensical. Because fall down, and fall over are both phrasal verbs that describe the process of falling to the ground. Whereas the original sentence is being used to describe the movement of the persons hair. In particular, fell over his forehead sounds weird, as it sounds as if the tuft of hair tripped over his forehead.

It would be better to say ' a tuft of hair falling across his forehead.'' 'over' is not incorrect, but a little unnatural. If you cut off a tuft of hair and it fell down his forehead (and rest of this face), you can use 'down', but otherwise not.

Hello, You can say both fall across and fall over his forehead. There is a slight difference in how the hair appears. Across suggests in one direction. Over suggests covers the forehead, straight down. In the context of your example, fall down his forehead is not natural. Hope that helps. Best, Martha