Complex sentence: Her biological father was Charles-Guillaume Le Normant d'Étiolles, husband of the future marquise de Pompadour, who was not yet Louis XV's mistress at the birth of her daughter.
Split into simpler sentences: Her biological father was the future marquise de Pompadour's husband, Charles-Guillaume Le Normant d'Étiolles. Her mother was not yet Louis XV's mistress at the birth of her daughter.