"What will happen next" --- straightforward question. The speaker is asking what will happen, and the person spoken to may or may not know.
"What happens next"--- this implies that the situation is one which is familiar to the person being questioned. The speaker thinks that the person he's asking will know what USUALLY happens next.
"Good Lord, now the phones for the entire dispatch division are out of order. What in the world will happen next?"
"If I tell him no, what do you think will happen next?"
"Okay, so every Thursday the delivery truck comes. What happens next?"
"So, class, we add a zero and carry the four. What happens next?"
"If you give a mouse a cookie, you know what happens next, don't you?"
[native speaker, not a teacher]
Student or Learner