Although a French Roman Catholic, Bossuet was interested to appeal also to Protestant readers. He wrote some of his books deliberately to explain his views to both Catholics and Protestants, using a style accessible to both groups, and offensive to neither. He believed that Catholicism was correct, and Protestantism mistaken, and that rational persuasion can be used in discussing these two competing interpretations of the faith - not emotional appeals or violence.
Louis XIV liked his style, and so Bossuet became the teacher of Louis XIV’s son.
Bossuet then wrote, partially as a textbook for the future king, that the duties of absolute ruler are: promoting the welfare of state; fostering religion and justice as the good constitution for the welfare of society; making peace; opposing false religion; and being humble because political power is a gift.
Ultimately, Bossuet could not accept the harsh absolutism of Hobbes, and moved beyond it, stating that the royal authority was limited by (a) the king's duty to be paternal to his subjects, (b) the king's duty to behave rationally, and (c) the king's accountability to God, from Whom political power comes.