"I will see him next week."
は is usually not necessary. It just emphasizes the time as the topic of the sentence.
[来週、] [かれ]に [会います]
[next week,] [him]← [i will meet]
に indicates who you will meet with.
But if your answer is:
[かれは] [来週]に [会います]
[as for him] [next week]← [will meet]
then に indicates when you will meet this person.
I was specifically marked wrong for including the は particle (as in, 来週はかれに会います) -is there a specific reason it should not be used? Perhaps something to do with the fact that 会います requires an obligatory に particle and the は particle confuses the sentence?