My dream deciphered their true relationship - SPOILERS!

^Thank you for your thoughtful reply.

There is no doubt in my mind that jmc4769 has a correct interpretation. I only have one point to raise: it seems to me that the explanation about the boy's last name is a bit lacking. Embarrassment about having had a child out of wedlock doesn't really cover why she would only want the father to see his first name. If he is the father, and he knows the son is his son, then her insistence about concealing his surname this seems a little unnecessary, and the interpretation a little forced. And yet, this discussion, though it occurs early in the movie, is clearly important, and is re-emphasized by all the discussion about how to sign each particular copy of the book during the driving scene. So, then, how should we understand her insistence on keeping James ignorant about Julien's last name?

One possibility occurs to me: yes, James and Elle (is this really her name?) did get together as jmc4769 explains it, and then again five years before the film starts, with James certainly under the impression that Julien is his son. But perhaps Julien is not in fact his son, but the son of another man, the product of a relationship she had around the same time. This would explain why, in the discussion about the son's name, there is never any indication whether in fact the son has the same first name as his mother: perhaps it is a mystery we are meant to solve later in the film. For this to be true, for Julien to be the son of a man other than James, one element of jmc4769's explanation would have to be incorrect: they could not have lived together for the first year or so. But I am not convinced that there is reason to believe they did so. Yes, he knows about the incident where Elle fell asleep while driving. But he was not in the car at that time, so I am not sure why the story itself shows that they were a couple living together.

A possible objection to this idea would be that it is too artificial: there is no other evidence that she had a child with another man. This is true. But on the other hand, perhaps there is another reason to consider this theory. The explanation by jmc4769 is in the end fairly one-sided: the woman wants a relationship and marriage, and the man (who is probably married in England) refuses and is some species of jerk who has had nothing to do with the raising of his son, comes to visit his mistress on very rare occasions and ultimately believes that everyone should be able to live their lives "for themselves" (as he puts it). Her misery is due almost entirely to his lack of "responsibility" (as she accuses him at one point). But what if Julien is not his son, and Julien in fact took the name of his biological father (perhaps she was even married to another man at the time they got together, but concealed this from James)? In that case, the fact that James believes he is his son is because Elle has misleadingly allowed him to believe it, because whoever the real father is, now her ex, doesn't interest her and is considered by her to be unimportant: for her, she wants it to be that James is Julien's father (because she thinks that his "real" father, the "original", is not as good as the "copy"), just as she wants it to be that she is James's "real" woman.

I can understand resistance to this theory, because if it is true, nothing really points to it being a possibility except the discussion between mother and son about last names. Nevertheless, I think it provides a more coherent and comprehensive explanation of that small but important piece of dialogue. One advantage of the theory, however, is that it adds a little more balance to the portrayal of the protagonists: yes, James is certainly a jerk, protecting himself at all costs while keeping her hanging on in some way long after there is any hope for the relationship. But she too is flawed, using her son's existence as a kind of psychological weapon in the battle of their non-relationship (their third-rate "copy" of a relationship). And in this theory, perhaps they had both been married to other partners at the time they met and conceived a child, and perhaps, too, in that first meeting they both concealed their marital status from each other. To me this fits a little better with the facts, and the symmetry of it also fits with Kiarostami's dislike of simplistic moralising narratives.

Just an idea.

What is the group's interpretation of the languages they speak? I had a feeling that English and French had different meanings... French was more intimate, made them (especially her) look more vulnerable, so perhaps that is a clue into them being together in France earlier. Also, when they talked about the car incident, she did say something about driving every Sunday, which makes me think that they were not married.

Regardless of whether they were or were not, the film is a masterpiece in its execution. There isn't a single thing that is out of place - framing, camerawork, reflections, extras, sound, acting. I really enjoyed it.

"In the second half of the movie, they briefly and playfully pretend to be married (they apparently had an affair some years ago). But once they get to the restaurant, they quickly drop the role-playing and start arguing about what happened the night before."

Exactly so. One key moment in the film is the shot from behind the bar. We gaze past She at the table, through the window where we see the man talking on his phone. The barmaid believes she is looking at a married man (whose wife is seated in the bar) speaking to his mistress. If fact, the entire film makes perfect sense once we understand that the man is speaking to his wife and the woman at the table is his former mistress. The "copy" relationship has been mistaken for the "original."

Notions of perception and value are at the heart of the film. Especially noteworthy is the exchange in the museum where we see the forgery under glass. That this and other discussions are enhanced when viewing the film through the interpretation of current pretense based upon past involvement renders it the most compelling, logical and satisfying reading.

I think your version of 2 is consistent, but I don't think it's the only version of 2 that is, and it may not be the most satisfying version of 2.

Call yours 2a and this one 2b ...

They are complete strangers. She is attracted to him because he physically resembles her ex-husband, and she genuinely finds his book enormously engaging intellectually (agreeing and disagreeing with it strongly in different places). Once she gets to know him, she finds that he is very much like her ex-husband in terms of character -- not a surprise given how much she liked the book.

Everything that happens after they are mistaken for husband and wife is pure role-playing by both of them. They both stick with it because they find it therapeutic, psychologically illuminating. They challenge one another with bits and pieces of an invented shared past, which they create by drawing on their real pasts. This is not 100% realistic, but it is only slightly artificial in a way that's enormously common in cinema. So they are creating a certified copy of a marriage, and the film, by becoming much less realistic, is reminding us that it is a certified copy of reality.

Some examples of how the role playing works: it really was her 15th anniversary the night before, which she spent painfully alone. She combines that fact with a real, painful memory of her husband falling asleep on some other occasion (perhaps a 5th anniversary). She's not complaining to him about a real thing that happened between them; she is expressing her loneliness and grief to a stranger in a way that weirdly is easier by pretending that it did. He can identify with this story because he knows he has been guilty of the same thing, and of course his natural inclination will be to defend the "guy", but he also wants to make her feel better about what happened to her (probably not getting that it is a very old memory) ... so from his own past he summons up the falling asleep at the wheel story. And she immediately gets the point he is making, and argues with him as if the story had really happened.

They have many opportunities to essentially break the fourth wall and stop the role playing, and they sometimes nearly do ... when he is simply too worn out to play along when she has him look out the window of her honeymoon room, he simply says "I don't remember," which actually means "I've got nothing to contribute here, role-playing-wise ... we can only take this so far." The role-playing only stops when he reminds her he needs to be back by 9:00.

This is the interpretation I had as I was watching the movie, and it works really well in terms of explaining the performances. It may not work quite as well as yours, but I think this version, where the relationship they are constructing in the second half is a pure invention, is deeper artistically, and more tightly integrates the themes of the movie. I like the idea that in the first half, the actors are acting, and in the second half, the characters are acting ... giving us copies of copies. And the acting is psychologically illuminating for the characters in the same way that watching actors is illuminating for the audience.

Of course it stretches credulity that two people would role-play so intensely and consistently, so it requires the proverbial "willing suspension of disbelief." Compared to, say, a billionaire dressing up in a costume to fight crime, though, it's really not that much of a stretch.

I think both of these interpretations were intended.

Prepare your minds for a new scale of physical, scientific values, gentlemen.