Sorry to bump this guys, but I just now got some time to properly respond to it. Anyways, first off,
@Basileus_Komnenos, it depends on what your aiming for as a POD; something around Charles X's accession in 1824 or him fighting off the July Revolution? Because both are doable, just need a different set of circumstances. So I'll go with a 1824-ish change first, then detail the July Revolution POD.
Before I start, everyone needs to understand Charles X's goals. He never planned a full restoration of the absolutist Ancien Régime, with its built in seigneurial rights for the Nobility and Clerical privileges. That's a bad myth that's been perpetuated over the centuries. Charles knew that ship had sailed. Instead he favored a very strong constitutional monarchy. Look at the Ordinances of Saint Cloud; even at his most absolute he never attempted to strip the Parliament of its powers nor change the Chartre. In fact everything he did in July 1830 was within the powers granted to him by the Charte Constitutionnelle, so any accusation of illegal action was something thrown around by the opposition during and after the July Revolution. Instead his goal was the restoration of the
spirit of pre-revolutionary society as based on the traditional three estates. He and Polignac saw the Chamber of Peers as a bastion of a revived aristocracy consolidated by a renewed primogeniture on land inheritance, tried to restore the Church's role in education and excluded certain taxes (the patente, the window and door taxes) from the criteria of the tax threshold for eligibility to vote, to block as many of the bourgeois from the franchise as possible. In this Charles used the concept of monarchy espoused by Louis XVI in a speech to the Estates-General in 1789. Now that that's out of the way, I can get to the details.
First off, Charles X was in a very good place at his accession in 1824. He was quite popular at the time, enjoying public sympathy from the murder of his son Berri in 1820, while the regimé itself had reestablished its credentials in the successful intervention in Spain. At the legislative elections later that year, the Ultras won 96% of the vote, securing 417 out of 430 seats in the Chambre des Deputies. That these advantages were squandered in three years was pretty bad but not entirely Charles's fault. The controversial Émigré indemnity and Anti-Sacrilege acts both originated under Louis XVIII but were only introduced in the 1825 legislative session. These laws were never going to be popular but formed a core part of the Ultra program, so they would be introduced no matter who was King. I suppose you could move these two laws up a bit earlier, to 1823, that way its Louis XVIII that takes the hit, but that's all I can think of there. Aside from these laws, there were several avoidable mistakes taken in the early years of the reign that can be easily changed in Charles's favor; the back and forth on press censorship, the dismissal of Chateaubriand as Minister of Foreign Affairs and the failed attempt to reestablish primogeniture.
During the Restauration the government went back and forth over Press censorship; in 1814 the press was liberalized but censorship returned partially in December 1814 and fully after the Hundred days; then it was abolished under the liberal era of 1815-1820, under Decazes and Richelieu, restored it during the Ultra reaction in 1820, abandoned again at the governments objection in 1822, restored in 1826, abandoned it again in 1828 and attempted to restore it in 1830. Basically the Ultras wanted a controlled but free press (ignoring that major contradiction) and could never agree on a unified policy. So in my opinion the best bet would be to keep the 1820 censorship laws intact and simply change the enforcement to match the mood in the country. Or, if your only wanting a POD of 1824 or later, have the harsh 1826 "law of reason and love" stay on the books rather than being repealed in 1828 in an overture to the left. That way the liberal press stays as muzzled as possible and aren't able to sure up the country at large. Now the dismissal of Chateaubriand happened in the last months of Louis XVIII's reign but caused major damage to Charles X. Chateaubriand, besides being one of Franc's most famous 19th century writers, was also a major Royalist politician during the Restauration, serving as Foreign minister in the Villéle Ministry, where he was the major advocate of the Spanish intervention, against what the Prime Minister wanted. Despite its ultimate success, Villéle was unhappy with Chateaubriand and secured his dismissal over his lukewarm support of a conversion loan. This sent one of the most talented literary minds in France into opposition, where he became a major writer in liberal newspapers. So either keep Louis XVIII from dismissing him or get Charles X to find him a position in the government/Court to keep him from supporting the opposition. An even better solution would be to put him in charge of government newspapers, utilizing his talents to support the Government in the public sphere. Finally, the failed attempt in 1826 to restore primogeniture, the Law of Inheritance, was rejected by the Liberal Peers created during the liberal era, so have the King make some new Peers and get the law passed. This would be another victory for the Ultras, despite its unpopularity, and, going hand in hand with the Indemnity law, begins to restore the nobility to its pre-revolutionary dominance (in this the King was influenced by the British Peerages dominance and prestige).
Second; the real decline of Charles X's reign started in 1827. That's the year the Garde Nationale nearly revolted when the King reviewed it and the legislative election that broke the power of the Ultras. In April 1827 the King reviewed the Garde Nationale de Paris; the militia was hostile, shouted "Long live the Charter" and "down with the Ministers/Jesuits!", and nearly turned into a riot. The next day the King and Villéle disbanded, but didn't disarm, the Guard. This was the first major mistake. The weapons of the Guard resurfaced three years later during the July Revolution. Instead the King should have disarmed, but not disbanded, the Guard. This is what Napoléon I did. That keeps a revolutionary institution around (a plus for popularity) and removes a threat in the heart of Paris (another plus). The second mistake was the early election Villéle called in November 1827. Now the reason for the early election is unknown but its believed that Villéle saw the rising unpopularity of the Ultras and dissolved the Chambre as to either get a new seven-year mandate before the unpopularity got worse or to unite the Ultras in their fear of renewed liberalism. Either way, it failed miserably; the Ultras split between the Ultras and the super-Ultras while the Liberals gained 170 seats (very similar to the 1830 election in Britain that saw the Tories split over Catholic emancipation and the Whigs make major gains). Now there was no reason to call an election at that point: a change in the electoral law in 1821 meant that, instead of a fifth of the Deputies being up for election every year, they were all up for election every seven years (just like Great Britain). So Villéle had another four years to rebuilt the Ultras popularity and no need for an early election. So avoid calling an early election or wait until the Ultras popularity recovered before calling one.
I think these steps should quiet the domestic front for the time being and keep Charles away form the fateful missteps of appointing Polignac and issuing the ordinances. Long-term it should also help strengthen Restoration France, especially when combined with the popular conquest of Algeria (would still likely happen as it was mentioned off and on sense Napoléon's reign). I'll add additional posts on foreign affairs and a failed July Revolution POD later.
