The only legitimate extant line of Capetian descent is the House of Bourbon, whose main cadet line is that of the now differencied House of Orleans. Must of the people in the Western Hemisphere has heard at least once about this powerful royal family, however few of them know why they came to power and from who do they descend.
The true is that France (Their country of origin) has been ruled by the Capetian family since 987 (And since 1848 only de jure), a House whose lay of succession was under the principle of Agnatism, that means that only male line descendants of Hugh Capet (The founder of the House) could acceed to the throne.
Under this principle France was saved from being inherited by an english monarch (Edward III of England), and was able to continue being not only one of the most powerful countries of Europe, but also as a sovereign center of culture, arts, science and monarchist society.
Indeed the french court was for centuries the most wonderfull of all european ones, being a model to follow, founding its peak of influence and grandeur under the reign of the third Bourbon king of France, the great Sun King, Louis XIV that ruled from 1643 to 1715, to date the longest ever reign of an european monarch.
The Bourbon dynasty ruled from 1589 to 1792, and again from 1814 to 1830, with its cadet branch of Orleans usurping the power from 1830 to 1848, after that date there has no been a Capetian ruler of France since then, however the family is extant and waiting for their throne to be restored eventually (I hope so).
Let's explore a little bit of history and reveal how the Bourbons came to the throne. Louis IX (reigned 1226-1270) the ninth monarch of the Main line of the Capetian dynasty, had six sons, the youngest Robert was created Count of Clermont, with no hope of ever inheriting the throne, his elder brother Philip III succeeded Louis IX.
However for 1328 with the death of Charles IV without male issue, the Main line of the Capetian family became extinct, the succession ruled by Salic Law meant that the next monarch was the next most senior capetian, who was Philip, Count of Valois, grandson in the male line of Philip III of France, with his arrival to the throne, the House of Valois began its rule in France (However notice that even they took a different family name, they were still Capetians).
The main line of the Valois became extinct in 1498 with the death of Charles VII, at wich time the line passed to the branch of the Valois-Orleans in the person of Louis XII, great grandson of Charles V of France, his death without any direct male issue in 1515, left the succession open to yet another branch of the House of Valois, this time in the person of Francis I, great-great grandson of Charles V.
The new branch was known as Valois-Angouleme and it would be the last branch of the Valois to rule in France, it was a bad-lucked dynasty that ruled for less than a century, in 1589 with the death of Henry III of France (The last male line scion of the hole House of Valois), the succession was open again.
Up to this time, all legitimate branches of the Capetian dynasty were extinct but two, the Bourbons and the Courtenays, and there was a little problem, the heir of the Bourbons was a protestant and the Courtenays were in poverty and weren't even recognized as princes of the royal blood anymore (They descent was very distant, only descending from Louis VI of France in the male line).
Henry of Bourbon, already King of Navarre was by salic law the new king of France since 1589, however only after he converted to catholicism could really take control of his new and powerful realm, taking the name of Henry IV, the Bourbon era was born, and after the Courtenays became extinct in the male line in 1730, the House of Bourbon became the last branch of the Capetians, to the luck of all the monarchists the House could survive until nowadays with several branches.
However the collateral lines to Henry IV of France are now extinct, the Bourbon-Conde, Bourbon-Conti and Bourbon-Montpensier lines became extinct eventually, thus all current capetians are descended in the male line from Henry IV, other important male lines also became extinct with the pass of the centuries, for example the line of Louis XV and Louis XVI, the main line became extinct after the death of Henry V, Count of Chamboard in 1883, now the main line surviving is that descending from Philip V of Spain, grandson of Louis XIV.
The House of Orleans is now the most junior, only descending in the male line from Louis XIII, if they were to descend to the french throne, all the next branches would have to become extinct before: The Bourbons-France (In the person of Louis XX), the Bourbon-Spain, the Bourbons-Seville, the Bourbons-Two Sicilies, the Bourbons-Parma and the Bourbons-Parma-Nassau.
Now we are going to explore the genealogy of the Bourbons, Im going to share with you (My dear lectors) the line of descent from Hugh Capet to Louis XX our current Capetian heir.