The film follows four families, with different nationalities (French, German, Russian and American) but with the same passion for music, from the 1930s to the 1960s. The various story lines cross each other time and again in different places and times, with their own theme scores that evolve as time passes. The main event in the film is the Second World War, which throws the stories of the four musical families together and mixes their fates. Although all characters are fictional, many of them are loosely based on historical musical icons (Édith Piaf, Josephine Baker, Herbert von Karajan, Glenn Miller, Rudolf Nureyev, etc.) The Boléro dance sequence at the end brings all the threads together.

A flamboyant master criminal and several specialists stage an audacious scheme to capture the Eiffel Tower and hold as hostage one of its visitors, the U.S. President's mother, while the head of a UN security force tries to stop them.

Nada, named after a gang of Spanish anarchists, is a small, confused band of French terrorists. They kidnap the American ambassador after one of his regular visits to an exclusive brothel. The gang starts to quarrel amongst themselves as to the diplomat's fate, while the police purge suspects in their attempts to destroy the Nada faction. As the violence escalates on both sides, the States and the terrorists are forced to use one another's methods in an increasingly desperate and relentless conflict.