Final answer:
The name of the famous ensemble during the reign of Louis XIV is The Court Ballet, which was closely tied to the ceremonial functions of the royal court at the Palace of Versailles.
Step-by-step explanation:
The famous ensemble during the reign of Louis XIV is best described as The Court Ballet. Louis XIV, also known as the Sun King, was an avid patron of the arts and his court was known for its opulence and the splendor of its performances. During his lengthy reign, the King actively participated in the arts as a means to showcase his power and the glory of the French monarchy. The Palace of Versailles became the center for political power and the host of these lavish spectacles, including many ballets which were presided over by the King himself. This makes The Court Ballet the accurate name for the famous ensemble of the period, as it was integrally connected to the royal court and its ceremonial functions