I will try to explain the governance of Stuart England. The main answer is that the measures the French kings enacted to centralize their government weren't available in England, but it is also more complicated than that.

Firstly, the English kings did have a centralized state. By the seventeenth century, the manor courts had become far less powerful than they had been in the high medieval period. People were able to access legal redress through the king's courts at the assizes, quarter sessions in their counties, or through Chancery and Common Please in Westminster. These were all the king's courts and justice was administered in the king's name. The sheriffs and lords who enforced justice and kept the peace did so as representatives of the king (Cocklburn, History of the English Assizes). Over the course of the sixteenth and seventeenth centuries, English civil servants did become more professionalized. Ambassadors ceased being simply powerful members of court, and instead became experts in the customs and politics of their respective posts (eg, Thomas Roe - ODNB; Embassy of Sir Thomas Roe to the Court of the Great Mogul; and Dudley Carleton - Lee, Letters of Dudley Carleton and Letters from and to Sir Dudley Carleton, Knt: During His Embassy in Holland).

Both James and Charles were builders, and employed Inigo Jones as the surveyor of the King's works. Jones spent much of his time updating the palaces and churches around London to make them comparable to the royal architecture on the continent. Under the later Stuarts, Christopher Wren was famous for his supervision of the rebuilding of London after the Great Fire of 1666 (Kishlansky, A Monarchy Transformed; Colvin, History of the Kings Works Volume 4).

The main barrier preventing Stuart kings from establishing greater centralized control was their finances. I can't speak too much for the French, but English monarchs needed the consent of parliament to collect taxes. Consent to taxation had a long tradition in England, dating to before 1215, but as Susan Brigden puts it, consent was "enshrined" in Magna Carta (New Worlds, Lost Worlds, p. 14). One of the largest revolts against a king in England was against a tax imposed in 1381 (Dobson, Peasants Revolt). The reason that parliament had to consent to taxes was because Englishmen held to the belief that the king should "live of his own." That meant that funds for paying bureaucrats, diplomats, advisers, customs agents, certain funds for justices of the peace, and any armies that were assembled all had to come from the king's own wealth. The king was the largest landowner in England, but even with all the territory, it was impossible to extract enough wealth from the king's lands to pay all his expenses. The king's other means of raising money were through the customs, levys (such as ship money), loans from merchants and creditors, or (and this was an extreme measure) by selling lands. Even all of this was not enough to manage a fully functioning early modern state. Even Elizabeth failed to meet her day-to-day financial needs through customs, rents, and loans towards the end of her reign (Russel, King James VI and I and his English Parliaments Chapter 1).

Building on the king’s financial troubles, Englishmen had a strong attachment to their traditions and customs. By traditions and customs, I mean their relationships with the royal government and their legal jurisdictions. Places like the Palatinate of Durham, Marches of Wales, border counties with Scotland, Berwick-upon-Tweed all had special legal jurisdictions and liberties peculiar to their jurisdiction. Most of these laws were tacked on in an ad hoc fashion, rather than being rationally drawn out, as Campbell makes clear in his analysis of twelfth century England (Essays in Anglo-Saxon History, chapter 10). Although Campbell wrote about a time 500 years before the Stuarts, the legal jurisdictions and many of the customs adopted after the Conquest remained in effect through to the seventeenth century. The main changes were the addition of the assize courts, but even these had restricted effects in places like Durham.

So, in summary, the English kings lacked the necessary funds and means of acquiring capital that were available to monarchs on the continent. Englishmen also clung to their ancient liberties restricting bureaucratic centralization. English kings tried to rule by consent and coopting the authority of the local elites, rather than relying on a centralized system. Even so, the English were creating a centralized state over the course of the Stuart period, and (for the later Stuarts at least) attempted to imitate the French model.