In terms of literary reference, the term "Romance" is a hard one to pin down. The genre is not specific to a given time or place; it is rather a theme throughout the history of literature. A classic example is Mallory's Le Morte d'Arthur, the legend of King Arthur. Most of the works that scholars would describe as Romances were based on folk tales and written down from the 12th through 14th centuries, mostly in France. However, the term can comfortably be applied to works from more recent eras.
Broadly speaking, the elements of a Romance can be considered: Quest, the centrality of love as a plot and character motivation, a mixture of immorality with an allegiance to chivalric values, a narrative packed with events, stock characters, and religion. Each of these elements is employed to great effect in The Three Musketeers.
Quest: the story is centered on some quest or goal, some action. It is an adventure, toward a certain end, which culminates in the success of the mission.
Love: in Romance, love is not viewed skeptically; rather, it is taken as a powerful and true force which drives people to do anything, and motivates their actions.
Immorality: the characters in a Romance, heroes as well as villains, often behave in ways which are bare-facedly amoral and wrong. One of the great characteristics of the Romance is this immorality oddly juxtaposed with allegiance to chivalric virtue.
Chivalry: the heroes in any Romance are guided by the ideals of Chivalry, a moral code that has its origins in medieval knighthood. Many Romances are legends about knights; the King Arthur is in many ways the archetypal Romance. Chivalry entails defending one's honor at all costs, to the death if necessary. It also entails treating women's honor similarly--a chivalric man must protect the body and honor of a woman with his life.
Narrative Eventfulness: the Romance, following its heroes' pursuit of their Quest, is packed with events and exciting, dramatic encounters. In fact, a Romance is often so crowded with events that, judged by modern standards, it can seem monotonous in its continual action. Dumas certainly uses the Romance's eventfulness, but he avoids the pitfall of boring eventfulness with effective pacing and composition.
The Romance's eventfulness affects the construction of the story as a whole. In many cases, the plot of a Romance doesn't begin, develop, and climax, but instead just sort of continues, going on and on. This characteristic is entirely evident in Dumas’s work--shielded by the fact of his magazine installment publication format, The Three Musketeers, although well paced and entertaining, doesn't have the same recognizable story "beats" that a modern adventure novel has.
Stock Characters: the traditional Romance relies on common and recognizable, rather than individual, characters. Dumas uses stock characters at times--the greedy innkeeper, the aging, discontented wife, etc. However, although there are certainly recognizable characteristics in some of his central players, Dumas’s main characters are vivid, original, and compellingly enough drawn to achieve great individuality.
Religion: religious themes are an intimate part of the archetypal Romance. The Arthur legends, for instance, draw on a great deal of fable and mysticism, but Christianity is also a strong presence, particularly in the central story of the Holy Grail. Dumas does not involve more mystical religious elements into his story, but rather, in a clever spin on the standard Romantic usage, makes religion an integral part of his story on two fronts. First it uses the Cardinal's presence as the primary antagonist of part I, and the presence of his heroes at the siege of La Rochelle throughout part II, a siege that was part of the Cardinal's Catholic war against the Protestants.