You can read the synopsis of the film on the other reviews present. Let me, on the other hand, focus on one scene which captures the beauty, intelligence and genius of Le Mepris.
The scene in question is in the bedroom between Piccoli and Bardot at the beginning of the film. It is likely they have just made love and Bardot (Camille) embarks on reassuring herself the love of her husband through a series of questions about her body. This portrayal of love gives us a feeling of heart-warming gratitude to Godard for delivering us from the fog of blockbuster, commercialised half-baked notions of love. This is, however, not the only way in which Godard strives to be different.
Let us look at lighting, music and camera. This tender scene is filmed with a strong red filter to enhance the impact of love. The hypnotising soundtrack dutifully plays over the images unfolding before us. The camera begins with a steady shot of the couple in bed. Nothing to write home about, I suppose. Except the red filter first changes to natural lighting, then to blue. When a piece from the soundtrack comes to an end, it does not coincide with the end of the scene as is usually the case, but rather the latter continues with all its intensity in silence. At other times the music becomes so loud we cannot hear the dialogue. The camera, having performed its common tasks of presenting the scene embarks on a close-up amble of Camille's nude body as if it had a mind of its own.
All the above techniques are deliberately engineered by Godard to make the spectator snap out of his passiveness. He is telling us to be independant, to react against being told how things are, in this case love. Incidentally, let us not forget that the physical love-making between Bardot and Piccoli is absent in this scene. Think about how hard a commercial movie will painfully try to film its obligatory love-scene in a constantly novel way to realise how significant this is.
Although nearly 40 years old now, Le Mepris remains and will remain fresh and inspiring for many years to come. The film is a necessary antidote to today's multiplexes and as relevant in the present cinematic climate to film-making in the 1960's.