I was put in touch with an alumnus in my city and we arranged over email to meet up in person at a cafe. It was a very relaxed and casual conversation, but she had a list of questions she needed to ask (must be something provided by the adcom):
1) Run me through your resume, particularly why you picked each role or changed jobs.
2) Tell me about a leadership experience you had.
3) Tell me about a time you experienced culture shock.
4) Why do you want to do an MBA and why at INSEAD?
5) What are your goals post-MBA?
After those questions, it was just a casual conversation where I could ask her anything and she gave very honest answers and also just asked a few follow up questions about my profile that she was personally curious about. Overall, a very friendly and conversational interview!