Adventure, Coming-Of-Age, Historical Fiction
Sword fighting + damsels in distress + narrow escapes from death = an adventure story. In The Three Musketeers, all the elements of a proper adventure story are present. But that would be way too easy for a writer of Dumas' calibre.
To make it more complicated, the adventures all act as a coming-of-age for a young Gascon gentleman named D’Artagnan who is eager to prove himself in the sophisticated world of Paris.
Providing the backdrop to all this adventuring and coming-of-age are various real and imagined historical events such as the siege of La Rochelle and the assassination of the Duke of Buckingham. So there you have it: The Three Musketeers as an adventure story, coming-of-age novel, and historical fiction.