What was the royal French residence and seat of government established by King Louis XIV, designed with gardens?

The royal French residence and seat of government established by King Louis XIV, known for its grand gardens and elaborate architecture, is Versailles. Louis XIV, often referred to as the Sun King, transformed Versailles from a hunting lodge into a symbol of absolute monarchy and a reflection of the power of the French state. The palace features numerous opulent rooms, extensive galleries, and the famous Hall of Mirrors, in addition to its meticulously designed gardens created by landscape architect André Le Nôtre.

The gardens of Versailles are particularly noteworthy for their structured design, including fountains, statues, and geometric layouts, embodying the ideals of French formal garden design from the 17th century. This design approach was revolutionary at the time and helped to convey the grandeur and control associated with the king's rule.

While the other options, such as Château de Fontainebleau, Château de Chambord, and Château de Chantilly, are also significant French châteaux with their own rich histories and architectural importance, they do not align with the specific context of being the royal seat of government as established by Louis XIV. Versailles stands out for its role as a center of political power and culture during the French monarchy.