Final answer:
The French generals believed they needed to conquer Mexico following the interests of Mexican conservatives and the ambitions of the French empire, culminating in the short-lived rule of Maximilian.
Step-by-step explanation:
The French generals believed they needed to take over Mexico as it was the will of the Mexican conservatives and the French empire. Napoleon III of France saw an opportunity to establish a French presence in the Americas during the American Civil War, believing the U.S. distraction would allow for successful intervention in Mexico. Despite initial setbacks, including the unexpected defeat at the Battle of Puebla on May 5, 1862, the French eventually established a regime under Maximilian, brother of the Austrian Emperor, which lasted until 1867 when it was overthrown by Mexican liberals led by Benito Juárez and Maximilian was executed.