As the poet Jacques Prévert said:

        Louis I
        Louis II
        Louis III
        Louis IV
        Louis V
        Louis VI
        Louis VII
        Louis VIII
        Louis IX
        Louis X (dit le Hutin) (called le Hutin)
        Louis XI
        Louis XII
        Louis XIII
        Louis XIV
        Louis XV
        Louis XVI
        Louis XVII
        Louis XVIII
        et plus personne plus rien...
        qu'est-ce que c'est que ces gens-là
        qui ne sont pas foutus 
        de compter jusqu'à vingt ?
                and nobody any more, nothing...
                who are these guys
                who ain't able
                to count until twenty?

What is remarkable about the French monarchs is that, between 987 and 1848, the same family ruled France. During the French Revolution, Louis XVI was called "Louis Capet" during his trial because Hugues Capet, 800 years before, was his direct ancestor.

No king ever came from another country. Many countries invaded France, but for a short period, and the legitimate king always regained his throne eventually. It may explain many things about France, including its strong feeling of being a nation (as opposed to a race) and its so-called arrogance.

From 987 to 1792, i.e during more than 800 years, the succession rules were strictly followed. Sometimes (but quite rarely) a king died without a legitimate heir, i.e a son, so that a brother, an uncle or a cousin had to become king. In three occasions, three brothers were kings one after the other:

  1. Louis X, Philip V and Charles IV between 1314 and 1328. The fact that during more than three centuries (987 - 1314), every king of France had a son who outlived him and became a king is very important, because it helped them to build a nation. While most of Europe was subject to instability and wars whenever a king died without a heir, in France the legitimacy of the new king was rarely questioned.
  2. François II, Charles IX and Henri III between 1559 and 1589. Note that one of the rare succession crisis in French history occurred when Henri III died without a heir. Henri IV had to fight to take the crown. He was a protestant, and had to become catholic: "Paris is worth a mass", as he allegedly said.
  3. Louis XVI, Louis XVIII and Charles X between 1774 and 1830, who ended the Bourbon Dynasty.

Louis-Philippe (1830-1848) was a distant cousin, and his accession to the throne was not legitimate. His father was a "régicide", i.e he had voted for the death penalty when Louis XVI was put to trial in 1793.

Other short facts:

  • Louis XIV was king during 72 years (more than Queen Victoria), and outlived his sons and grand-sons. Louis XV was his great grand son, and he outlived his sons too, so that France had only two kings in 131 years.
  • There is no Louis XVII, because the son of Louis XVI died in a jail during the Revolution. Louis XVIII considered that, according to the succession rules, Louis XVII had been king after Louis XVI died, so he decided he would be #18 and not #17.
  • In the same way, Napoleon III decided that Napoleon I's son had been emperor after his father abdicated in 1815, although the king (Louis XVIII) had regained the throne.
  • Since mauler has used English names in his list of French kings above, here is how English names map to French names:
Henry       -> Henri
Hugh Capet  -> Hugues Capet
John        -> Jean
Merovich    -> Mérovée
Odo         -> Eudes
Philip      -> Philippe

Oh, yeah, there are still pretenders to the throne in France. One of them is Louis XX, a descendent of Louis XIV and the most legitimate of all with regard to succession rules. Another one is the Count of Paris, a descendent of Louis-Philippe. And I'm not speaking about those who claim that Louis XVII, just like Elvis, did not die in jail during the Revolution and had children afterwards...

Thanks LeoDV for a correction about Capet, which was not Hugues Capet's family name because family names did not exist then...