When teaching grammar, you need to look at the context and time frame of the action when it happened. Underlining “told” as a clue here is wrong. What happens outside of ” ” does not affect the time frame of the speech.

In the speech itself, the teacher was talking to the parent about the fall that happened to the daughter. At that point in time, the child has already fallen which is why the teacher was talking in the past tense and had to use “had” to show that. 

‘Fall’ in this sentence is a noun, not a verb.

I think it should be ‘had‘ because the question is ‘had a … fall‘. The fall happened in the past. Hence, it should be simple past tense.