Final answer:
King Louis XIV ruled New France with a centralized authoritarian system, and there was little self-governance for colonists. The French crown promoted mercantilism, but not religious freedom, as part of its colony management strategy.
Step-by-step explanation:
To understand how King Louis XIV ruled New France, we should look into the absolute monarchy of France during his reign. The first statement is correct; Louis XIV ruled New France with a centralized and authoritarian system of government, reflective of his absolute monarchy in France. This centralized control extended across the ocean, meaning that New France had a highly structured, royal colony status with limited self-governance for colonists. Therefore, the second statement is incorrect; the colonists did not have a significant degree of self-governance.
While Louis XIV was a Catholic monarch intent on furthering Catholicism, the third statement's claim about religious freedom does not align with the overarching goal of spreading Catholic influence, so religious tolerance was limited. Lastly, the fourth statement is correct: under Louis XIV and his finance minister, Jean-Baptiste Colbert, policies were implemented to foster economic growth and development, emphasizing mercantilism in New France.