Disc Two

It's a "Certified Copy" of the first disc.

Just Kidding.

It contains some extra stuff, including a documentary about the Director and how he cast the movie. Apparently Juliette Binoche was very involved in taking this from a story the Director told her to getting it made as a movie.

It doesn't solve the central mystery of their true relationship, but it does point out what I had considered the key scene- the coffee shop where the proprietor starts asking questions about their "marriage".