Where It All Goes Down
Paris, France and Nearby Estates during the late 1700s.
Almost all of the action in Les Liaisons Dangereuses happens in the homes of wealthy individuals, in the city of Paris or nearby. A few scenes occur in carriages, at the opera, and at a convent.
As the narration is done by the major characters writing to each other, the setting is seldom described in much detail. After all, the characters themselves don't need to be told what the locations look or sound like. They're there. They know.
More important to the setting is the time period. The novel was written before the start of the French Revolution, in which the decadent world of the aristocracy came crashing down, but Chodelos de Laclos knew a doomed society when he saw one.
Critics of the novel disagree about whether or not the novel was meant as a criticism of French society at the time, but there's no doubt that Laclos did a masterful job of describing the bored, wealthy, titled people with nothing much to do but go to the opera or their country estates and meddle in the lives of others. To be fashionable, to see and be seen with the right people, was the extent of their values.