I don't think that having been a soldier or having experienced dangerous situations frees you from fear. War hero or not - there were moments when Michael was scared. In the restaurant scene he was scared to death. In the bathroom he's almost panicking when he doesn't find the gun first. When he sits down we can almost hear his heart pounding.
The novel says: "he must have been scared because he was glad he was no longer standing on his legs. They had gone weak with trembling."