Hugo is oddly specific about when and where this story takes place. In fact, Time gets the first line of the novel: "Three hundred and forty-eight years, six months, and nineteen days ago, the good people of Paris awoke to the sound of all the bells pealing in the three districts of the Cité, the Université, and the Ville" (I.I.1). The emphasis here is on the past—the really, really precise past. You won't find any "A long time ago, in a galaxy far far away…" here. We as readers get the sense that if Hugo is going through the trouble to be so darn exact about the date, then we're actually about to read some "real" history. The setting helps us out in this regard; after all, who hasn't heard of that magical, make-believe kingdom of Paris, France?
But why 1482? Why not 1481, or 1483, or 1526, or 1642? Because Hugo is so specific, it behooves us to really look at what was going on around 1482 that would make it relevant to the story. So here's your "What was happening in 1482 in France?" cheat sheet:
The Hundred Years' War between England and France had ended in 1453 (it's referred to occasionally in the novel), and Louis XI had ascended to the French throne in 1423. He died in 1483, as the novel mentions, which means that the story takes place at the very tail end of his reign. Louis really wanted to consolidate the power of the monarchy, because as it was France was ruled by some really powerful dukes who were basically mini-kings. A particular thorn in Louis's side was the Duke of Burgundy, Charles the Bold, who owned a big chunk of the east of France, including Flanders. Louis defeated Charles and got these territories in 1477, but there were some complications with this guy Maximilian I, so basically the Dauphin (who was twelve years old) and Maximilian's daughter, Margaret of Flanders (who was three), had to be betrothed so that Louis could keep this territory.
This history might sound try and distant and pseudo-relevant, but it's actually all over the novel. Think about it: the first scene of the novel is of Gringoire's play, which deals with the Dauphin's marriage to Margaret of Flanders and is attended by some big-wig Flemish ambassadors; and there is a long chapter towards the novel's climax of Louis XI strutting around the cage of one of his opponents and talking about how France really ought to have just one king. This novel is fraught with discussions about centralized state power, who has jurisdiction over what, who determines justice, etc.
But Hugo also has the benefit of hindsight, and he loves to use the events of the past as harbingers of the future. So, for Hugo in 1831, the major recent historical event would have definitely been the French Revolution of 1789. In that year the Bastille, which, in the novel, is where Louis sits comfortably as he talks about the power of the monarchy, was stormed and destroyed by a mob. Four years later, the King of France (Louis XVI) was executed via guillotine. But then along comes a little general named Napoleon Bonaparte, who crowns himself emperor from 1804 to 1815. After Napoleon, however, France is back to monarchs again.
So really, Hugo seems to be contrasting a period in history when state power was absolute, to a period when that absolute power had been seriously called into question. Hugo also loves to contrast the physical layout and architecture of the Paris of yesteryear with the Paris of the 1830's, showing us how impossible it is to stop the tide of change from working its magic/destruction. There is also a whole chapter devoted to the printing replacing architecture in the fifteenth century, so 1482 also represents a major turning point in history when the status quo of the church is going to be severely shaken up (see our Symbols, Imagery, Allegory section for more on why the printing press is so great).
In short, time is really important to this novel. Check out our Themes section if you want some more convincing.