The Capetian dynasty ruled France from 987 until the French Revolution, when Louis XVI went to the guillotine in 1793 under the name of Citizen Louis Capet. He was officially part of the Bourbon dynasty, which had succeeded the Valois dynasty, but they were male-line Capetians all the time, just descended from younger brothers.
As I discussed in an earlier post, the Capetian dynasty succeeded the Carolingian dynasty in France--the most famous Carolingian of course was Charlemagne, who had been crowned Roman emperor in 800. Hugh Capet was not strictly speaking the first king of his family, because both his great-uncle Odo and his grandfather Robert I had been kings (succeeded for a few years by the final hurrah of the Carolingians), but from 987 on there was an unbroken line of kings descended directly from Hugh.
The most famous medieval Capetian king was probably Louis IX, or Saint Louis, after whom the American city is named (pictured above). He determinedly sought peace and justice in his kingdom, trying to impose what we would call chivalrous behavior on his knights (things like not killing someone without giving them a chance to fight back, or, best of all, not even killing them a little bit). He went on Crusade twice, though both excursions were disasters.
On the first of his Crusades, they decided to set up a base camp in Egypt, then attack the Holy Land from there. Instead he was captured and held for ransom. On the second, they decided that Egypt was too dangerous to go right in, so they decided to set up a base camp in Libya from which to attack Egypt--with predictable results. When the old king and one of his sons were killed, the surviving French boiled him up so that they could get his bones to take home for burial.
His son, Philip IV, got Saint Louis declared a saint. Philip also is responsible for starting the Avignon papacy by completely intimidating the popes (see more here). He disbanded the Templars, in the hope of getting their treasure, but unfortunately for him they had no treasure. Philip IV is called "the Fair" for his blond hair, not his personality.
The story goes that as the head of the Templars was dying under torture, he cursed Philip, that he would not have sons to succeed. As Philip had three sons, he laughed this off. But all three died in quick succession after their father, leading both to the Valois dynasty and to the Hundred Years War. After a great deal of unpleasantness--the Hundred Years War actually lasted over a century--Joan of Arc inspired the French to finally defeat the English.
At this point, the French kings started down the road toward absolutism. Louis XI (1461-1483) trusted no one, and filled his court with intrigue and spies. He was known as "the Spider." He was also intensely religious and always had at least a few dozen bits of saints' relics pinned to his clothing, for protection. Although true absolutism really only came about in the seventeenth century, with Louis XIV, the trend was there.