What movies are they watching ?

In episode 7, Lee DaEum takes Lee JaeAh to the movies and from then on, they start pretending that she has a future. I'd love to know the title of the movie, they are watching, and whether the scene shown on screen relates to that particular development . 

Also, what other movies, if any, are they going to watch in this drama ? What other nods to cinema did you spot ? 

EDIT : Found it, it's the Green Ray by Rohmer