Wikipedia, as always, has a nice summary of what Alphaville is about:
Enjoy. It's a really weird movie (in a good way), if you haven't seen it before.
Alphaville combines the genres of dystopian science fiction and film noir. Although set far in the future on another planet, there are no special effects or elaborate sets; instead, the film was shot in real locations in Paris, the night-time streets of the capital becoming the streets of Alphaville, while modernist glass and concrete buildings represent the city's interiors. In addition, the characters refer to twentieth century events; for example, the hero describes himself as a Guadalcanal veteran.
Eddie Constantine plays Lemmy Caution, a trenchcoat-wearing secret agent. Constantine had already played this role in dozens of previous films; the character was originally created by British pulp novelist Peter Cheyney. However, in Alphaville, director Jean-Luc Godard moves Caution away from his usual twentieth century setting, and places him in a futuristic sci-fi dystopia, the technocratic dictatorship of Alphaville.