What's Happening in History During the Novel? It's 1625-1628 in France. 

Other Nations 

The First Folio was first published in 1623. Charles I is the King of England. 
In 1620, the Mayflower lands in America. 
In 1625, the Dutch settle New Amsterdam. 

Invention 

It's not the Age of Enlightenment yet. 
Galileo Galilei has published a book using his new invention, the microscope. The Catholic Church will prohibit his book, Dialogue Concerning the Two Chief World Systems ​1633. 

Religious Tension 

The major wars fought in this period were mostly about Protestant vs. Catholic. There's more about this over in the Basics. 

What About When Dumas Penned the Novel? 1844 in France. 

Dumas wrote The Three Musketeers in a time of great uncertainty in France. France, a major colonial power, was still trying to figure out how to best rule its people. The Industrial Revolution heightened the sense of great change, and created greater wealth disparities than in the centuries past. An uneasy time, The Three Musketeers serves as a great method of escapism for its readers. However, it's a clever form of escapism as Dumas is able to do it in a way that still comments on French society of 1844. 

The French had a long series of Revolutions, starting in then eighteenth century. The first French Revolution, the one that Jefferson wants to fund and Hamilton does not, was 1789-1799. This revolution led to the rise of Napoleon Bonaparte, for whom Dumas' father fought. The revolution closest to the the of the publication of Three Musketeers is the one that the events of Les Miserables is based around,  the events of Les Miserables primarily take place in 1832, twelve years before the publication of The Three Musketeers. In 1830, The July Revolution had put the Orléanist monarchy on the throne, under the popular “Citizen King” Louis-Philippe (but a friend of Dumas). Louis-Philippe ruled until 1848, when he was forced to abdicate the throne (February Revolution) for France's' first elected president, Napoleon III (the nephew of Napoleon Bonaparte). Exactly four years later he suspended the elected assembly, establishing the Second French Empire, which lasted until 1870-- Louis Napoleon was the last French monarch. 

Alexander Dumas lived from 1802-1870, experiencing much of this change personally. It is easy to see why Dumas' novel about escaping back to an idealized time was so popular. The serialized novel provided a method of escape for its readers. The popularity of the novel is akin to the popularity of comic books during World War II--it served as a method to ease tension, take the reader far out of their ordinary life, and present a world in which the good guy always won. 

The novel also shows a deep sense of pride in country and heritage, something that the French have proved they have a lot of time and time again. The novel also presents history as a cycle that repeats itself, The Musketeers is a cautionary tale and a satirical one, a political one, and a smart one.