In their short night together (before both need to depart Vienna, possibly to never see each other again), Celine (Julie Delpy) and Jesse (Ethan Hawke) live in perpetual fear of the inevitable hardship or fight that will tear them apart. But it's an argument that brings them together. A middle-aged couple's loud quarrel drives Celine toward Jesse. They first connect over trying to figure out what that veteran couple were feuding about. This opening scene provides us with the film's thesis - it's an exploration of life's transitory nature that's both melancholy and celebratory, built upon contradictions.
The protagonists are supremely self-aware, understanding the narratives that we want to use to categorize their lives. Jesse, an American in Europe, seems to want a Hemingway moment, a chance to absorb some old world knowledge while adventuring anonymously. He's quick to note, however, that this is not the case. He bought a Eurail pass to kill time before a flight that will get him out of Europe (and away from an ex-girlfriend who he went to see). And yet, he's getting his Hemingway moment, discussing philosophy and culture while romancing a French woman in Vienna. Celine is also aware of another narrative that she might fit into - that of the French girl that Jesse will sleep with and brag about to his friends back in the States. She says that she won't sleep with him to avoid fitting into that narrative and cheapening their encounter. Yet, she ends up on top of him and it's suggested that they do have sex. They argue over whether each gender has its own mission - and what that mission is - before contenting themselves that men and women have had the same discussion for thousands of years without any real answer. This constant questioning of their actions and roles makes for funny moments, but it also creates realistic characters. While we consider ourselves intelligent beings, we're all familiar with disobeying the rational boundaries that we set for ourselves.