First, I should say that I'm a high school history teacher so I'm only an amateur historian, at best. My apologies if my question doesn't make sense.
I teach AP European history, and make a big deal out of the shift from deductive medieval reasoning to the inductive reasoning devised during the Scientific Revolution. Now, typically this shift is explained as leading to the scientific conception of political theory starting with Hobbes and Locke. Regarding Hobbes, his assertion was that powerful centralized monarchy was ideal as decided by the people due to their volatile nature. Is there evidence that this thought process was popular in Louis XIV's absolutist France, thereby making that society one who's loyalty was based of Hobbes's inductive theories?
Or, was the French population sold on Louis XIV's regime based on the deductive assertion of Divine Right Monarchy?
The general French population wasn't concerned with Hobbes, no. He was discussed amongst French philosophical circles, but other than that there isn't a lot of evidence that he was influential in any way. I'm of the opinion that Leviathan was meant for an English audience given the fact that Hobbes was writing and living during the Civil War, and it was his first work to be written in English (wasn't published in Latin till almost a decade later). Absolutism, in theory, had been around well before Louis was ever coronated. James I published polemical writings about divine right in the late 16th century (True Law of Free Monarchies and the Basilikon Doron) that looked similar to what Louis ultimately created. I'd argue that Louis was much more influenced by the events of the Fronde than anything else. So back to the people (Sorry I went off on a tangent), Louis had a whole team of people whose sole job was to cultivate a popular image of the King. I'd recommend the book The Fabrication of Louis XIV by Peter Burke. It is a fantastic explanation of the cult of the sun king.