For example, would a 16th century French king have known anything about the ways of life of an average peasant, or were they completely deluded about how the majority of their subjects lived?
I'm sorry nobody has replied to this yet, but I will say it's a hard question to answer clearly. I'm going to take a stab at this, hopefully I can give you some insight into how the social divisions in these cases worked. I will tell you, though, that I am more of an English historian than a French one, so my insight into sixteenth century France is comparatively limited. Now, there's an important distinction I want to make here. A sixteenth century monarch really isn't quite early modern, yet. You might say he or she is early early modern, or late late renaissance. This matters, because it helps to define how monarchy often functioned. Henry IV of France, for example, could be described as a "persuader-in-chief" who, while laying some of the groundwork for French absolutism, worked by glad-handing and cajoling his nobility. This meant he was fairly mobile and exposed to many levels of social strata, because it was in his best interest. But a king like Louis XIV, while not totally static nor isolated, certainly created levels of hierarchy and social difference around himself in order to better control his nobility. This eventually created social insolation that kings like Louis XV and XVI did not really understand how to pierce, and as a result, were distanced from the general population. This distancing was also a part of a general social trend dividing the elite from the plebeians.
I said that this is a hard question to answer because monarchs were not clueless about the lives of their peasants, but-- not having the experience of living as a peasant-- they didn't have an easy basis for understanding the "peasant experience." Whenever an early modern monarch (or a late Renaissance monarch) traveled, as they did often, they would see the peasants at work. They understood that the lives of the peasants was largely defined by agriculture in one way or another, so they knew the agricultural calendar that restricted activities like warmaking, etc. The monarchs also understood the limitations of food preservation to some extent, in that the peasants went through periods of hardship and abundance throughout the year.
In many places in Europe the nobility were pretty firmly immersed in the lives of the peasantry. They lived better and were served by the peasantry, sure, but they also partied with the peasants, played the role of the Carneval idiot, etc. I'm not saying that the local lord showed up at a public house and drank with his peasants like they're his mates, but the physical and cultural distance wasn't that great-- it was the social distance that differentiated the elites from everyone else. And by social distance I mean the exercise of power. The elites, all the way up to the monarch, had judicial power, military power, and the power to tax. Of course, they were limited by custom and the fact that with this power came responsibilities to their peasants.
BUT, the fact remains that though a monarch or noble may have had a pretty fair understanding of peasant life, he could avoid some of the dangers of that life by exercising his right to power. At the baldest, during a time of famine a monarch could use his armed might to assure himself that he had enough food. This wasn't always the best idea, but it gives you a good example.
So, did a monarch understand peasant life? In an academic sense, sure. In an intimate, personal sense, probably not.
Some sources: