Vigot is the French police officer charged with investigating Pyle's death. Well, investigating might not be the right word. He's supposed to file a report, but not look too deeply into the matter. Pyle was an American working in Vietnam on both disclosed and undisclosed business. Vigot has the sense to know that the truth could upset and embarrass powerful people in Vietnam, France, and America. He finds a kindred spirit in Blaise Pascal, the French writer of religion and paradoxes.
He's something of a Colombo. He knows more than he lets on and he observes what people would like to keep hidden. He tells Fowler:
You are not a criminal, but I would like to know why you lied to me. You saw Pyle the night he died. (4.1.28)
He suspects Fowler, to some degree, not only because of some holes in his story, but also because Fowler isn't angry with him for the continual questions. Keenly perceptive, he can tell Fowler feels guilt about something.