Using pour emphasizes that the duration of her stay in France will be 3 days. With pendant you are speaking about the duration of the entire trip, not just her stay in France.

Jules, 

I suspect the reason ‘pendant’ was used is probably because this was translated as present tense. However, in English ‘is going…’ is ambiguous without context, as ‘ am going to go’ is often abbreviated. In everyday speech it could mean she is on her way right now, going soon or sometime further in the future. 

Regardless the ‘three days’ are definitely in the future as the English sentence unambiguously means she is not there yet, and the duration expressed is in the future, and “intended”. 

(I still have no idea what the somewhat cryptic comment in the lesson - ‘the suggestion of intent’ - means in practice, as anything planned to extend into the future is ‘intended’ and can change, at least theoretically). 

You most certainly can use ‘pour trois jours’ here - my wife is a qualified French English translator and would have done so. However, pendant is also correct here.

The distinction suggested in the response of a different meaning between ‘pour’ and ‘pendant’ does not hold up well here - indeed if ‘pour’ applies to the time in France more specifically, that favours its use in the answer, as that reflects the English sentence exactly. 

Bottom line, don’t sweat it too much, but remember that ‘pour (duration)’ is for ‘future’ durations, so excludes ‘events’ that have happened or are currently in progress, while ‘pendant’ can be used for either past completed or future ‘intended’ events.