Both movies revolve around a woman, or young woman, caught between two men, and her confusion with regards to whom she loves, if she loves anyone at all. This seems to be the point of focus for Godard--not to question whether the woman loves Guy A or Guy B, but rather, to question love as an entity in itself. What is love? Why is it so transient? And yet why do we feel compelled to keep it, chain it, lock it, and throw away the key? It is this existential, philosophical quandary which interests Godard, in addition to his observations that love (sex?) for women is both a form of currency and a prison simultaneously.
In Band of Outsiders, Odile is the object of affection for two classmates, Arthur and Franz. I say "object of affection," because both Arthur and Franz have a competition for who will basically own Odile, their callousness towards her becoming more apparent as the narrative progresses. Odile chooses Arthur at first, and we know this by the fact that she will take a cigarette that is offered by Arthur, but not by Franz. This is Godard's way of saying that ownership, or property, is the modus operandi of the film, and the Capitalistic world in general; as he will later whisper as the narrator in Two or Three Things I Know About Her, "Maybe an object is what serves as a link between subjects." It is not a stretch to say that Odile becomes just another object which Arthur uses to get to what he and Franz set out for in the beginning: the stash of money at the house where Odile house-sits for an elderly wealthy couple.
Even the opening of the movie tells us Odile's inner turmoil at feeling the dichotomy between attraction and imprisonment. The film begins with a fast montage cutting the three faces of the protagonists, each person staring intensely in a direction. In the beginning, Franz stares right to left. His eyeline does not connect with Odile, whose eyelines do connect with Arthur. The look on their faces can be read as romantic. Slowly, Franz shifts his gaze to Arthur and stares daggers. Then, Odile shifts her gaze downward and seems unsettled. She looks right to left and sees Franz. The conflict of the film has been established: two men fighting over a woman, who feels the loneliness of objectification.
Also, in many of the shots in the movie, Odile is framed in the middle, between the two men. In the famous dance bar sequence where the three of them dance for a very extended period of time as the sound drops out and the omniscient narrator tells us the thoughts of our protagonists (a technique which Godard seems to have mastered by this film), Odile dances between Arthur and Franz. Even as they run "freely" through the Louvre in another iconic scene, Odile is still trapped between the two guys.
One may argue that the affect of the film does not support this reading, and indeed, the film and the characters have a carefree, ramshackle feel. At one point, Franz says something akin to, "Let's form a plan." Odile looks straight into the camera and says, "Why?" This is a meta-moment where he's both challenging cinema's perceived need to have a narrative, but also the idea that plans are needed in real life. However, as the film progresses, Arthur and Franz "carefree" attitude starts to look a lot more nihilistic and dangerous. When the money is not where Odile says it was, the characters tie her up and we feel a very real threat, the threat of violence against Odile in the name of money (not unlike the end of Vivre Sa Vie) that basically serves to retroactively alter the perceived "recklessness of youth" that came before.
In Une Femme Mariee, Charlotte's husband at one point slaps her and basically rapes her (off-screen) after she refuses to turn off a record which he asked her not to play. Though the presentation of the rape is not physically forceful, it is still acknowledged as such, and reminds us that rape is not always a physical violence -- it can be a psychological one as well. Similarly, there is a scene where Charlotte's maid describes to her a sexual encounter she had with her husband where he left her "black and blue," and yet she says it while smiling and laughing and cleaning the dishwasher. Godard seems particularly interested in the violence and prostitution of the domestic household in this film. Though, like Godard's definition of prostitution (anyone who does something they don't want to), I gather that his definition of violence is similarly wide. If I had to guess, violence is intimately tied to this definition of prostitution and would go something like this: any repercussions or negative consequences that come from attempting to escape the prison of Capitalism.
When Charlotte cheats on her husband, it is not because she doesn't love her husband anymore. Perhaps she does not, but that is not the point. We feel that Charlotte cheats on her husband as an expression of her freedom to choose her own fate in this life, to do what feels pleasurable. But the question of love hangs over the film like a drifting cloud. Why do we love? And how do we know we are in love? Godard shoots the scenes with Charlotte and her lover (and most of the movie) in close-ups which isolate parts of her body. Her head seems severed from the rest of her body. Her legs seem to exist on their own. Her midsection. Her lips. Her hands. The film seems to be objectifying her body, even as questions of love are put forth.
Pleasure and love are intimately intertwined in this film. So intertwined, in fact, that Godard seems to be asking us, "Is there a difference?" Charlotte used to feel pleasure with her husband, but now something feels missing and she wonders whether she still loves him. Her boyfriend pleasures her, and she admits that she loves him. However, how long can pleasure last? As Charlotte is waiting to meet up with her lover, she flips through a magazine where advertisement after advertisement shows women in brassieres, seductively smiling at us and teasing the prospect of love. What is love to Capitalism, but just another commodity? And what is a commodity, but just something sold to us, promising increased happiness? Godard seems to be saying that love, like pleasure, is just another temporary spike in happiness, just another lie sold to us by the Capitalistic structures in place. In fact, Capitalism benefits from a transient love, a love that jumps from one person to the next and relies on our desires to impress, to be new.
In the end of the film after Charlotte sleeps with her lover, she wonders whether he actually loves her, and how he knows that he does. She does not trust love. "It is over," she says at the end of the film. She has accepted the transience of existence and has succumbed to her fate, a fate determined by Capitalism.
I would just like to add as an addendum that these movies show Godard as having very strong control over the formal techniques which he explored in his first six films, almost to the point where the rough edges have been sanded down. The films no longer feel jarring, or experimental, but rather smoothly operating by the new rules that Godard had written for cinema. I have no doubt that he again tries to jut himself out of his own comfort zone in the films that come after.