There are a bunch of standard, boring things you should probably know about the coach, like their running/coaching history, but it might be interesting to pose a couple of hypothetical questions to them regarding situations that may arise...
How will they deal with attendance issues? Attitude issues? Selecting the top 7 for the championship meet? Disciplinary action if someone gets in trouble at or out of school? Some elitist kid who wants to be coached by a personal coach but still race for the school?
I don't know if any of these issues are relevant at your school, but come up with some detailed scenarios and see what they say. The more convoluted the scenario, the better.
good luck