Research the producer so you know what films he has worked on before, what his general background is and any other interesting trivia about him. This helps you determine the best questions to ask.
Write down a list of basic questions for the producer but leave enough time in the interview for you to ask improvised questions based on the producer's previous answers. You should be prepared with some questions to ask before beginning the interview so you're not wasting the producer's time.
Ask the producer how she got into producing. Acting, directing and other specialized jobs in the film industry usually have schools that specialize in them or classes to learn the trade whereas producing really doesn't. As a result, producers often have varied stories about how they broke into the industry.
Discuss the previous films the producer has worked on briefly to get his perceptions on the various projects and what he has learned from each of them.
Talk about any current films on which the producer is working. The producer is likely doing the interview at least partially to promote the new film so a good portion of the interview should be dedicated to discussing it.
Inquire about any funny stories or surprising moments from the producer's career. Everyone has different stories to tell and the producer may be able to give you a memorable incident to close out your interview.