Cléo de 5 à 7 (1961) dir. Agnès Varda
Varda's Cléo is part of the 'Left Bank' of the French New Wave. The Left Bank, including Alain Resnais (Hiroshima mon amour, Last Year at Marienbad) and Chris Marker (La Jetée) was more political and more explicitly existential than the Right Bank, which included Jean-Luc Godard (Breathless, Vivre sa vie) and François Truffaut (The 400 Blows, Jules et Jim).
You can find an easy exception in Godard's (Alphaville) and Truffaut's (Fahrenheit 451) political films, but theirs are more abstractly Marxist and less concerned with contemporary left-wing politics that the Left Bank is. Varda includes a radio newscast of the war in Algeria in her film, implicating French filmgoers in the same neglect that Cléo has for anyone outside herself.
Cléo vanity isn't exactly a moral failing. As a beautiful female singer, she's subject to the male gaze even more than most women. She doesn't see herself internally; she only looks at herself through a mirror, trying to see herself as a man would see her.
But, in the traditional of existential fiction, that all changes when Cléo is faced with the prospect of her own death. She seeks an escape, but cannot find one. Perhaps most cruelly, she learns that her own mortality doesn't affect other people in the way it affects her. This is driven home by the nonchalant, accidental way she learns her fate.
It takes less than an hour and a half (the film obeys the unity of time) for evidence of Cléo's character change to surface. She finds a real conversation, and real companionship with the soldier she meets at the park. She'll still be dealt with on the surface by most people - but now, she has hope for an authentic life.
Cléo de 5 à 7 is #553 on the 2012 edition of the TSPDT 1,000 list I’m blogging through. I’ve now seen 452.