Warning: Wikipedia contains spoilers
The plot is simple - Lemmy Caution (played by Constantine), an 'outland' agent, arrives in the futuristic city of Alphaville to search for missing agent Henry Dickson. The city is under the control of Professor von Braun and run by the Alpha 60 computer system. Love, poetry, emotion and so on are outlawed for the inhabitants of the city creating an inhuman and alienated society. Caution enlists Natascha (Anna Karina), the daughter of von Braun, to help him.
Godard uses this straightforward sci-fi scenario to produce a bizarre, messy film deliberately unbalanced in its action. The film is dark in terms of physical lighting as well as the elliptic philosophical dialogue and cynical humour. Caution is a parody of an American private eye: wearing the trench-coat and shooting people carelessly he is defiantly erratic in the logical city, dominated by the Alpha 60 computer which he has sworn to destroy. Caution's love for Natascha introduces emotion and unpredictability into the city that the computer has crafted in its own image.
The film was shot in 1960s Paris, the night-time streets of the capital becoming Alphaville with modernist glass and concrete being used for interiors, reflecting the problems of the future onto contemporary France. There are no special effects to enhance the science fiction elements of the film. In a rather clumsy move Godard apparently wanted to title the film Tarzan versus IBM.