What do you think are Fache's motivations in the book, and what do you think it says about him as a man?

As Langdon observes early in the book, Fache openly displays his religion. However, it's not revealed until much later on that Fache is The Teacher who is controlling the actions of Silas and Aringarosa. Although Fache's devotion to his religious beliefs might seem admirable under other circumstances, his religious views are causing him to put a deadly chain of events into action. That goes against everything that is expected of a police officer. So, in my opinion, Fache has no business being an officer.