Anna Karina, who died earlier this week aged 79 of cancer, will be remembered for her singular contribution to French cinema. Her achievements were legion. In 1961, she starred in Jean-Luc Godard’s Une Femme Est Une Femme. Their marriage later that year led to one of the great wife-husband collaborations, bringing eight collaborations including Vivre Sa Vie and Pierrot Le Fou. They stand alongside some of the greatest films of the nouvelle vague – Agnes Varda’s Cleo de 5 a 7 and Francois Truffaut’s Les Quatre Cents Coups.

But it is for her performance in Godard’s 1965 film Alphaville that I will remember her best. The hero of the piece is a proto-Deckard, Lemmy Caution, played by Eddy Constantine. Godard cast him after watching him play cops in American B-movies. He visits Alphaville, where life is controlled by a super-computer, Alpha 60, as a journalist-observer – he hails from the “Outlands,” which have so far avoided the yoke of artificial intelligence. Alphaville is a dreary city populated by blank-faced prostitutes and Gestapo-style apparatchiks. All human feeling is expressly forbidden on authority of the super-computer – a man is shot by a firing squad for crying at his wife’s death.

Caution meets one of Alpha 60’s programmers, Natacha von Braun, played by Anna Karina, and soon falls in love. At first, she cannot love him back. After all, what could love mean to a model citizen of Alphaville? It’s a society conditioned by Alpha 60 according to the computer’s hyper-efficient conception of the “ultimate good”. In such a place, there can be no encounter with something or someone other than oneself, no love.

Caution lends her a book of poetry he has brought with him, Paul Eluard’s Capitale de la douleur. After reading first in halting style, she confidently says: “De loin en loin dit la haine. De proche, en proche, dit l’amour.” Soon the whole Alphaville system comes crashing down (yes, that’s what poetry can do!) and Caution and von Braun escape, driving away from the city to the Outlands as fast as they can manage. Natacha turns to Caution and says: “Je vous aime”.

Moments in cinema have a funny way of clarifying certain moods and they exert a powerful force on what Milan Kundera called “poetic memory,” the part of the brain in which metaphors, images and stories are collected that “make our lives beautiful.”

Bob Dylan in his ridiculously epic song Brownsville Girl perorates for 11 minutes straight on “a movie I seen one time”. “I don’t remember who I was or where I was bound / All I remember about it was it starred Gregory Peck,” he sings plaintively.

The American essayist Joan Didion, in her essay “John Wayne: a love song” recalls watching his Westerns for the first time, “that summer of 1943 while the hot wind blew outside.” For Didion, Wayne, in his bravado and the high romance of his characters, “suggested another world… a place where a man could move free, could make his own code and live by it.” In one of his flicks he tells his girl that he would build her a house “at the bend in the river where the cottonwoods grow.”

Didion continues: “Although the men I have known have had many virtues… they have never been John Wayne, and they have never taken me to that bend in the river where the cottonwoods grow. Deep in that part of my heart where the artificial rain forever falls, that is still the line I wait to hear.”

I’m not quite suggesting that, for Didion’s John Wayne you should read Benn’s Anna Karina, but there really was something extraordinary about Anna Karina’s performance in Alphaville – who wouldn’t want to be speeding onwards, danger behind, the Outlands ahead, the tunnel lights slipping along one by one, with a spiralling Tristan and Isolde Liebestod-style soundtrack crashing on top of it all? And then… Je vous aime!