I get the idea of a family crypt, but I've read that the Ducal Crypt contains hearts and viscera while the bodies are buried elsewhere. What was the point and meaning of this ritual, and was it a common ritual in Europe among other royal families? Was this sort of burial common for lower class folks?
I have an earlier answer from a similar question about the Bourbons, if you're interested. I do touch on the Holy Roman Empire, too!
Death was one of those situations where the ideals of medieval theology clashed with practical expediency. The doctrine of resurrection of the body led many theologians to demand corpses remain intact. On the other hand, by the high Middle Ages, noble crusaders dying in the Near East wished to be buried in consecrated (church) ground back in Europe. Evisceration and rudimentary embalming was necessary for transporting a corpse for such a lengthy period of travel. The coroners of later medieval England, too, almost certainly performed basic autopsy as part of their task of determining whether sudden deaths were accident or murder.
For the upper classes of France and England, and very select groups within the Holy Roman Empire (the bishop-princes of Wurzburg are the most famous), separate burial of certain organs took on a new importance: politics. There are some early cases, like Emperor Henry III in 1056 who wanted his heart and entrails (a common pairing, as we will see) buried next to his daughter Matilda.
But it's the later Middle Ages that really entrench the practice. Separating organs--particularly the heavily symbolic ones such as the heart--allowed the elite to literally be in two places at once, at least in death. It was important for the monasteries where they were buried and also for their legacies. Additionally, the need to be buried in multiple places came to serve as a status symbol for the elite. A peasant had one home; there was no need for his body to be buried at Fontrevault and his heart at Rouen. The use of heart burial as a status symbol only increased when the papacy tried to squelch the practice: securing the special dispensation to eviscerate a corpse was a status symbol in its own right!
So the pattern is well established by the time we get to the Bourbon dynasty on the cusp of Counter-Reformation in the 16th century. And the practice of dividing up the bodies of the elite remains just as, maybe more important at this time. One of the major patterns we can see in heart/entrail/body burials by the late Middle Ages is the placating of different religious orders. The body will go to an abbey (and its graveyard) associated with one of the traditional monastic orders, the Benedictines or Cistercians. Nobles tended to prefer that their heart went to the mendicant orders. (N.b: I don't know why, and any thoughts on the matter I might have would be speculation.) The Catholic Reformation introduces a vast new array of religious orders to patronize. The Jesuits were key in the skyrocketing of heart burials in the 16th-17th century.
One final factor to consider in the French case, specifically, is the assassination of Henri IV in 1610, who was actually the first Bourbon king to have his heart buried by the Jesuits. Since Henri had been a Protestant who converted to Catholicism, and also to mark their own role as royal heart-bearers, the Jesuits made a massive deal out of the 'funeral procession' for just the heart. Weis-Krejci calls it a "bombastic political spectacle." The publicity really established this practice in the popular mindset. (Although not the Jesuits' role, which begins to decline later in the 17th century.)
And finally, the early modern era witnesses new attention to establishing the royal family as sacred and separate (although there are plenty of sainted kings and queens in the Middle Ages). This development coincides with the late medieval=>early modern development of the cultus (veneration/devotion) of the Sacred Heart of Jesus. Venerating the heart of Jesus, and to some extent Mary, cast new important on the heart itself--as evidenced by the Jesuits' big parade/promotion of Henri IV's heart, almost a bigger deal than over the body itself. In promoting the hearts of the royals, therefore, their successors and those who benefited from royal patronage tapped into this current of devotion and drew an important parallel between the hearts of the earthly king and the heavenly King.
Further reading: