Sofia Coppola's influence on the film is seen in its subtlety. Bill Murray is a naturally funny person and this is played up in his movie star persona as the character of Bob in the film. He's charming, funny and enjoyable to be around--and Charlotte is attracted to this about him. But it is also what makes him a star, his ability to make people feels things that he wants them to feel. Thus, casting the part to Murray was a direct influence on the storyline's success.
Coppola's use of framing is also a major influence on the film as well. An example is her shot of Bob and Charlotte at the hotel bar. There is a single seat between them and they appear to have a connection but what can be felt as you watch the scene is a vast distance between the two of them. This is a remarkable feat as it is a subtle touch that is made possible in Coppola's capable hands. She's able to bring forth the inner-life of the characters in a way that tells the story and makes the audience feels a great deal more than what is merely seen on the screen.
Coppola also influenced the film by writing its screenplay. It is based on her experiences abroad in Tokyo and specifically at the Park Hyatt Tokyo where many of the film's scenes are set. And Coppola has said that she was influenced by Humphrey Bogart and Lauren Bacall's relationship in The Big Sleep and that it was the mold for the relationship which she was after.
Finally, the final scene. Coppola creates a narrative that takes us to a single moment, a goodbye between Charlotte and Bob where he says something to her that we don't hear. This moment has gone down in film history, and its impact has a great deal of meaning to it because it can be interpreted in so many ways. To attempt to give it significance here would only be one of many interpretations of it, and that is the point the director wished to make. This is your story; what is being said?
