Why was Louis XIV of France able to rule as an absolute monarch, while Stuart kings of England could not?
Louis XIV (1638-1715) was indeed the iconic absolute monarch. His statement of "L'etat, c'est moi" (The State is me) sums up the extreme degree of the cult of personality and the concentration of political power he cultivated.
Part of the reason Louis could rule as he did was that France remained a Catholic country through the turmoil of the Protestant Reformation. Inherent in the Catholicism of the time was the cosmology of the Great Chain of Being; God was at the top of the hierarchy followed by the hosts of heaven, down to the kings that by Divine Right could rule the lesser men under them. France, even though it became an economic power during Louis' reign, still retained this Mediaeval construct.
Not so in England, which had a long history of limiting monarchical power, beginning with the Magna Carta in 1215. By the 1640's, England had temporarily done away with the monarchy. England, being Protestant, had no allegiance to the Church or Mediaeval cultural forms, and during the Glorious Revolution (1688) the succession of monarchy had been achieved by laws, not arms. England had by this time developed a strong legislative branch of government in Parliament, through which the nobility could govern. A strong Parliament effectively split the powers of government; no person nor entity could both legislate and execute laws. No such institution evolved in France under Louis until his death; as the embodiment of the State, he was the lawmaker and executor.
In summary, the nobles in England got stronger and checked the power of the monarch, whereas in France the reverse happened -- the monarchy got stronger and checked the power of the nobles.
The Glorious Revolution marked the end of the Stuart dynasty, not really a step on the way to limiting its power. When James I, the first Stuart king, took the throne, he attempted to assert the powers of an absolute monarch, as outlined in his famous tract "Trew Law of Free Monarchy." There was indeed a tradition of Parliamentary limits on the monarchy, but it was hardly imposed peacefully as kings respected the concessions of King John in the Magna Carta.
It was established, rather, in the process of a bloody civil war and the execution of Charles I. After more than a decade of Cromwell's rule, Charles II took over and brutally attempted to reestablish monarchical rule even as dissidents plotted against him. These plots reached a crescendo in the 1670s with the Rye House conspiracy, and when James II took the throne, he faced constant opposition before the so-called Glorious Revolution. Finally, the old nobility decidedly did not get stronger in England, they were weakened, and replaced by a growing middle class and landed gentry that asserted its supremacy through the House of Commons.