A Woman is a Woman (1961)

Angela is a burlesque dancer for a small club in Paris.  She and her lover Emile live a modest life in a small city apartment, in which they share moments of quiet domesticity and also melodramatic conflict.  Angela wants to have a child, but Emile isn't ready to make the commitment, and though she tries to persuade him he refuses to bend to her will.  They fight in overly dramatic fashion, breaking the fourth wall and bowing to the audience before commencing their fight, and pulling books from the shelves and using their titles to articulate their respective points.  Emile's best friend, Alfred, reveals that he is in love with Angela as well, something which Emile knows all too well already.  

Exasperated by Angela's pleas for a baby, Emile tells her to sleep with Alfred if she wants a child so badly.  Angela calls Emile's bluff and heads over to Alfred's apartment, in which we see her conflictingly undress as she mulls her decision.  Upon returning home, Angela finds Emile visibly upset yet still very much in love with her.  He comes to the realization that she will push their relationship to the brink in order to have this baby, and he decides that the only way to continue on is to make love to her so that the child would possibly be his.  Though they don't explicitly say whether or not Angela actually slept with Alfred, it is my belief that she did not and was simply using the threat as a gambit to force Emile's hand.

Jean-Luc Godard's "A Woman is a Woman" embodies everything that I've come to know about the dawning of the psychedelic era in France.  The young, bohemian lifestyle of the two lovers, the playfulness in which they act out the mundanities of young domestic life.  Godard really has fun with this picture, as he utilizes a grab bag of camera tricks and technical quirks in this cinematic world he creates.  Background noise is sometimes amplified to unrealistic levels or removed entirely from scenes, the impossibly gorgeous Angela (Anna Karina) breaks out in song in a scene that seems plucked from a musical.  The genre boundaries here aren't clearly defined, making for a completely unique film experience.  As previously mentioned, the two lovers break the fourth wall in order to address the audience, bowing for the performance of their quarrel before engaging in it.  Jump cuts are used as characters change outfits simply by walking through a door, and Angela flips an egg in the air and returns minutes later to catch it.  Non-diegetic music and dialog is inserted in certain portions of the film, creating a world in which the viewer feels anything is possible.  Godard even name checks his most popular film "Breathless" in one scene, with a character refusing to leave the house because the film is going to be shown on TV later.  This film is probably my favorite of Godard's simply for the fact that you can almost see him enjoying the filmmaking experience as you take it in, it's the cinematic equivalent of witnessing Jimi Hendrix in the throes of passion in the midst of a solo.  Godard is riffing here.