(Changed John II to John III, since there was already a John II of France before the list's POD.)
What if Henri III of France managed to have a son?
1589 - 1634: Charles X (House of Valois) [1]
1634 - 1640: Charles XI (House of Valois) [2]
1640 - 1685: Henri IV (House of Valois) [3]
1685 - 1701: Jacques (House of Valois) [4]
1701 - 1726: Charles XII (House of Valois) [5]
1726 - 1739: Philippe VII (House of Habsburg) [6]
1739 - 1760: Venceslas I (House of Habsburg) [7]
1760 - 1783: Venceslas II (House of Habsburg) [8]
1783 - 1835: Christophe (House of Habsburg) [9]
1835 - 1850: Dominique (House of Habsburg) [10]
1850 - 1860: Civil War [11]
1860 - 1890: John III (House of Burgundy) [12]
1890 - 1939: Charles XIII (House of Burgundy) [13]
1939 - 1977: Henri V (House of Burgundy) [14]
1977 - 1998: John IV (House of Burgundy) [15]
[1] Charles X, the only son of Henri III became King at just fourteen years old after the assassination of his father at the hands of an insane monk. France was riven with tensions due to the issue of religion and politics. Namely the Protestant Huguenots who were led by Henry III of Navarre and the nominal heir after Charles, and the fanatic Catholic factions led by the House of Guise and Henry I, Duke of Guise. The regency was headed by his mother, Louise of Lorraine, who was quickly under the thumb of Charles, Cardinal de Bourbon (and an alternate Catholic heir). The regency of the Cardinal merely caused more friction between the factions that exploded with the assassination of the Cardinal on the King's 16th birthday. To stem the tide Charles proclaimed his majority and was convinced by his mother to issue the Edict of Nantes, a proclamation granting the Protestants freedom to worship privately, but not publicly. Charles X was fascinated by the trade goods that were starting to come into the Kingdom from Asia and set up the French East Trading Company, unknowingly setting the stage for France's role as a major trading empire. He also defended the Dutch Republic from Spanish invasion, hoping to one day peel off the Spanish Netherlands (RL Belgium and Luxembourg) from Spain's control, though this didn't occur in Charles's reign. Charles married a daughter of James I and she bore him two sons, the eldest Charles became king upon his father's death at age 59.
[2] Charles XI had all the appearance of wishing to continue his father's policies of religious tolerance and trade expansion. He increased trade with further flung countries in the east, and reinforced the Edict of Nantes, which granted Protestants the right of private worship. However, he died suddenly in 1640, officially of smallpox, but there were rumors of him being poisoned by an agent of the Vatican. His wife had borne him only a daughter, Anne, and so he was succeeded by his younger brother, Henri.
[3] Henri IV, was also taught to continue his father and elder brother's policies of religious tolerance and trade expansion. Although the government continued to claim the previous King's death was smallpox, it did not help to hide the deteriorating relations with the increasingly pro-Hapsburg Papal States. His rule also saw conflict with the Spanish and the Austrians over the Duchy of Lorraine, which culminated in the War of the Lorrainian Succession that would begin 3 months shy of Henri's death. He bore 5 children, 2 of which were sons, and the eldest, James would succeed him.
[4] Jaqcues (in English referred to as James or "James the Catholic") upon gaining the throne his main aim was for peace and was able to bring peace a year into his reign, ad sealed the peace with the marriage to Maria Antonia of Austria and had three sons and two daughters.
He was the more pious the his father, uncle and grandfather and some say he was the Pope's popular choice, his reign saw the Catholic church rise up to be more powerful to the anger of the Protestants.
While, he let his first two son to marry their choice, his third son Charles, was married to his cousin Anne, while his daughters Françoise was married to Ferdinand III of HRE's son Leopold (Future Leopold I) and Marie was married to Philip IV of Spain's son John.
[5] Charles was James's third and youngest son, and became heir after his two older brother's "untimely" death. "Untimely" meaning he assassinated them and everyone knew it. Charles led with an iron fist, which led to him being dubbed , Charles le Fer "Charles the Iron". He was universally hated and feared, even by foreign rulers. This culminated when in 1723, a coalition led by Spain and Austria attacked France to dethrone King Charles. They succeeded in 1726, when he was replaced by Philippe VII.
[6] Philippe VII is primarily remembered for his ability to compromise. He was as Catholic as the next Habsburg, but he also recognized that France had a sizable Protestant community. Whether he viewed them as heretics was neither here nor there, because he knew that to continue to persecute and harass them would mean continued hostilities throughout France. So he restored the Edict of Nantes, and also provided Protestants equal protections under the law. He was already married when he became King, and left the throne to his son, Wenzel. When he died, he left France more at peace than it had been in nearly a century, but whether or not the country would permanently accept the Habsburgs remained to be seen.
[7] Born in Prague where his father had resided prior to Philippe's ascension of the French throne, Venceslas had, perhaps, resided in more places across the continent than any of his contemporaries. Prague to Vienna to Paris, and of course the Grand Tour he made which traveled to Madrid, London, and even the far-flung Ruthenian Kiev. At news of his father's illness he returned to court and brought with him a host of intellectuals and thinkers, primarily from the Germanies and Italy, but including companions he had collected all over. This group, called the Tuileries Conclave, for they most often met the monarch in Tuileries Palace, acted in an advisory capacity and influenced Venceslas in toward major reforms. The two most notable being Venceslas's decree that the Esates-General should begin to meet annually to advise the monarch and his plans to restructure and expand Paris, overseen by Tuileres conclavist George Frideric Haendel, a German extracted thinker and the father of modern Urbanism.
[8] Venceslas II continued what his father started and generally was seen as the most successful monarch of his generation. While that isn't a truly huge feat as the other most successful monarch was the rebellion riddled Spanish monarch. He ended up marrying Queen Henrietta of England and had three daughters and one son upon his death: Mary (b.1750), Joanna (b.1753), Anne (b.1758) and Charles (b.1759). He died in his sleep as a very fat 55 year old.
[9] Christophe, the five year old son of Dauphin Charles took the throne after his father and grandfather both died before him. His reign would oversee the expansion of the French colonial Empire into Africa and even deeper into Asia than ever before. He also presided over a time of great change in Europe as the Spanish Habsburgs were overthrown in the Spanish Revolution that saw the establishment of a radical republican government, while at the same time the British lost control of their colonies and witnessed the birth of the Confederation of American States (CAS). These changes threatened the Old Order and while Christophe gave refuge to his Spanish relations, he was unable to place them back on the Spanish throne even after the 'First Spanish Republic' collapsed, it was simply replaced by a dictatorship. He instead encouraged them to reestablish themselves in their holdings in Italy, namely Naples. Christophe wasn't above taking advantage of things though and seized as many Spanish holdings as he could in the name of keeping them out of the hands of 'the radicals', effectively making France the largest Empire in the world. But this came with a price, the Spanish practiced slavery extensively in their colonies, whereas there was a movement in France to end the practice in the French holdings. The issue of slavery in the New World would grow more controversial and wouldn't be resolved in Christophe's reign, instead that was left in the hands of his only living child, Dominique.
[10] Dominique was the only surviving child out of 10 stillbirths, thus being called 'The Desired' as heir. As Dominique took the throne, the former Spanish colonies declared their independence from both Spain and France, dragging both countries in a costly 9-way war against France, radical Spain, and 7 colonial factions mostly based on nationality, but having the right to slavery as a common cause. By the time of Dominique's premature death due to an explosive kitchen incident, only the former Spanish East Indies were secured by France, as the other colonies were too vast and distant that they stretched both the French and Spanish forces thin.
[11] After the death of Dominique, there was no clear heir to the throne of France and as a result a Civil War broke out with several nobles with distant connections to the royal family fighting it out to determine the new king. Eventually, John of Burgundy wins a decisive battle in July 1860 and is crowned in September 1860 as King of France.
[12] After John of Burgundy won the civil war, he immediately secured his legitimacy by marrying a granddaughter of Princess Mary of Habsburg, the eldest daughter of Venceslas II. Named "The Victorious," he immediately imprisoned or banished all other claimants to the throne unless they swore fealty to him. His reign is characterized by the flourishing of the trading with the Turkish Sultanate and expansion of the realm through the conquest of Africa. Under him, France easily became one of the wealthiest and most powerful of empires. In New Year's Eve 1890, he died of a brain aneurysm after lingering for two weeks because of a stroke. He left 5 daughters and twin sons, the eldest of which, named Charles, succeeded him as Charles XIII.
[13] Charles XIII ruled for 49 years and oversaw a period of unrest which began when a French noble was assassinated as he was visiting the Turkish Sultanate. This began the Great War (1899-1925) in which several countries of Europe were left ruined messes as the French fought with the Turks. Finally ending the war with a decisive victory in Thrace, Charles XIII forced a humiliating treaty upon the Turkish rulers which stated that the Kingdom of France gained a great amount of territory from the Sultanate in return for releasing the Sultan, who been captured in the final battle of the war. After the end of the war, Charles XIII ruled peacefully for 14 years, dying in 1939 to be succeeded by his son, Henri V.
[14] Henri V broke down many barriers during the course of his reign. He broke with tradition in his personal life by marrying not a princess from another country, but a French commoner, Gabrielle St. Claire. He also began a coalition among his fellow European rulers that put pressure on American nations who still denied civil rights to minorities, using trade embargos and other such methods as a method of protest. He proved quite popular for his views on racial equality, and there was much mourning when he died suddenly in his sleep in 1977, leaving his eldest son, John, to continue his line.
[15] King John IV continued his fathers policies, though presided over an era of revolutions in the African and Asian colonies. He managed to get a system in which those colonies remained associated states, but the Empire lost much of its prestige.