Here are a few things I found interesting:
Formal balls were by no means the only social dance events held at court. The opportunities for courtiers to dance were numerous and varied, ranging from informal evenings in the king's apartments to balletic presentations on stage. At one end of the spectrum were the so-called jours d'appartement, approximately three evenings a week during which the king opened his apartment in the chateau to his courtiers. Guests were free to wander from room to room, watching or taking part in the different entertainments each provided: gambling (the most popular), billiards (the king's favourite), music, dancing and lavish refreshments. (42)
Although the author notes that the amount of dancing at the court varied greatly over the years, depending on external events,
[during one active period, from] 10 September 1684 [to] 3 March 1685, the beginning of Lent, there were at the court alone: 1 grand bal; 9 masked balls; 16 appartements that definitely included dancing; 42 other appartements that almost certainly also offered dancing; and at least 2 evenings of comedy that included dancing between the acts by courtiers. This all adds up to approximately 70 opportunities for dancing during a 175-day period, or one every two to three days. (42)
Beyond all these, other members of the court held dancing events, especially during Carneval.
On the branle, courante, and menuet:
Formal balls were opened, and sometimes also closed, with branles [group dances]. . . . [Then] came a courante danced by the highest ranking couple. . . . Menuets were also done, and there seems to have been quite a long period during which the two dances coexisted at court balls [but] the transition. . . probably occurred during the early years of the 18th century. By 1719, at a ball given for the nine-year-old Louis XV, a menuet opened the ball, and by 1725 Pierre Rameau spoke of the courante as a dying, if not already dead, dance. His book makes it clear that the menuet was the principal social dance of the day and had been for some time. (45)
On the contredanse:
The other type of group social dance, the contredanse, was already very popular at the French court in the 1690s. . . . Their interest lay in the patterns and figures formed by the group of dancers rather than in the steps, which, although more codified than those of the English country dances, were simple and repetitious in comparison with the complex step patterns of the choreographed French dances. The contredanses were often done at appartements and masked balls. . . . During the reign of Louis XV contredanses were a well established part of formal balls. (46)
On the types of dances, divided between (not rigidly maintained) categories of social and theatrical dance:
The most common dances at balls, after the opening branles, were courantes, menuets, passepieds and contredanses. Judging from the choreographies in Feuillet notation that were published as ball dances, bourées, gavottes and rigaudons were also frequently found in the ballroom. Of a primarily theatrical character were the sarabande, gigue, forlana, loure, canarie, chaconne, passacaille and folies d'Espagne, although individual representatives of these dance types did establish themselves in the social dance repertoire as well. (48)