Another possibility : Louis XVIII or Charles X can't stand the idea of Orléans becoming their heir, and pass a law to block his way (like Louis XIV did for the Spanish branch). They edict, for example, that the son of a regicide can't inherit the crown.
The situation of succession in the first half of the nineteenth century was quite clear to everyone; the claims to the Crown of France came so striking when the throne was already gone. To understand this we must look to an event of OTL that sheds light on the issue of succession.
On 21 September 1824 King Charles X accorded to the Duke of Orléans the title of Royal Highness and conferred to the last of the Condé the title of Grand Master of France.
Charles X had thus affection for the Duke of Orleans, or at least self-interest for the good of France.
A bit of "color".
Since the Duke was only "His Most Serene Highness", when he was present at Court with his wife, the Duchess Marie-Amélie was announced for firstly with both doors of the salon open; when one door has been closed, the usher announced the Duke Louis-Philippe of Orléans.«Charles X fit dire par le grand maître des cérémonies qu'il avait donné ordre [...] de [...] effacer la fameuse et irritante distinction de la
famille et de la
maison, que Louis XVIII avait introduite et maintenue» (Antonetti).
The same situation of the Duchess of Angoulême, who before Louis XVIII's death, was more high-ranking than her husband, because she was daughter of a King (Louis XVI), and her husband was just only the nephew of the King: for example, when they were in front of a door, the duchess of Angoulême always was going before her husband (but with a slight difference with the Duke of Orléans, for the Duke of Angoulême the door was always completely open , because the rank difference was less distant between the Duchess and the Duke of Angoulême, daughter and nephew of Kings, while, on the other hand, between the Duchess Marie-Amélie and the Duke Louis-Philippe of Orléans the rank difference was greater, because she was daughter of a King, instead the duke was only a far descendant of Kings).
Also to bridge these differences in rank, five days after the death of Louis XVIII (16 September), after the accession to the throne, Charles X accorded the title of Royal Highness to Louis-Philippe and to all his children, and to Louis-Philippe's sister Adélaïde: when the Louis-Philippe himself said to the new king that Louis XVIII never wanted to bridge the gap, and Charles X responded: «I know. He had a little foible about this, some ideas which I don't think fair, but you must agree that your situation is a little awkward...» (from the "Journal" of the Duchess Marie-Amélie).
And also the King said:
«Je trouve que c'est plus conforme à l'état des choses ici, plus encore à celui de l'Europe».
The Duke of Orléans, now at height desired of his desires, thanked Charles X with effusions, professing an obsequious and enthusiastic respect for the King: and from the law of the «milliard des émigrés» («billion to the émigrés», Act on the émigrés' billion), the millions of indemnity to the emigres, the duke drew 14 million of francs...
Why this act?
Charles X with this act attempted to unify the House of Bourbon, because with the assassination of the Duke of Berry the House of Orléans was more likely to succeed to the throne.
The King The king explained to the duke the three reasons for this gesture:
1. you [ought be able to] collect the succession without difficulty, without embarrassment.
2. you know that there are people who dream of the Spanish branch, I do not think many, but you take on guard.
3. I am willing to help you do my best. I wish to spare at the France the heartbreak that would cause to it.
Why these worries?
It was clear to them the distinction between "famille et maison" (family and House) and "Couronne" (Crown): there is a clear distinction between the role of heir to the role of "Head of the House" and heir to the French throne.
It is a mistake to consider as a "only one thing" the Throne of France and the direction of the House of Bourbon.
Moreover, it is a mistake to base this discussion on the Treaty of Utrecht, the terms of which, of course, do not represent a commitment/obligation «for nobody by long time, by the eighteenth century».
The renunciation of Philip V of Spain: a prince who renounces, acting spontaneously or forcedly, at his rights, in reality he can actually fulfill the renunciation only for himself and not for his descendants; it is still questionable if he can renounce for himself, when this renunciation could mean a damage for the country concerned.
While allowing the personal renunciation of a prince, the descendants of him could will always claim their rights. It can renounce at personal rights, not at rights over-personal.
The question is this:
+ in Spain the Philip V's renunciations were made Fundamental Laws of the Kingdom by the same sovereign who convoked specifically for this the Cortes in March 1713. This means that, according to the spanish principles of legitimacy, no member of the descendants of Philip V has the right to the Throne of France.
If the renunciation was not declared Fundamental Law of the Kingdom, it could have been considered invalid the renunciation; but a Fundamental Law can be repealed only by the King and the Cortes.
+ instead, in France the renunciation is not Fundamental Laws of the Kingdom, because it has avoided to bring together the States General to the ratified, and the European diplomacy gave for good the ratification by the Parliament of Paris, which, as we know, was a juridical corporation, not an assembly of the Kingdom (probably because misled by the similarity/assonance with the English "Parliament").
The ratification by the Parliament of Paris has a only mere value testamentary or notarial.
In Spain only the King and the Cortes can cancel the renunciation allowing to a descendant of Philip V to claim the throne of France: if the King and the Cortes dispense to the renunciation an Infante who descendant by Philip V, this Infante could claim the throne of France.
The Throne of France, thus, in early nineteenth century it's up indisputably and unquestionably to the Orléans.
on the other hand, it's well understood that they can not call themselves Heads of the House of Bourbon, as long as they persist lines descended from Philip V: with the extinction of the elder branch founded by Louis Duke of Burgundy, grandson of Louis XIV and elder brother of Philip V of Spain, the branch of the same Philip V becomes the elder/oldest branch of the House (la branche aînée).
At the Head of the House of Bourbon corresponds the mastership/command of the Dynastic Chivalric Orders, namely the Order of Saint Louis, the Order of Saint Michael and the Order of the Holy Spirit.
In addition, the renunciations do not prevent, then, to a Spanish prince to exercise the Regency of France (the same Philip V tried to exercise it clashing with the Duke of Orléans).
«Il faut convenir que votre position est délicate. [...] Il est important pour vous et pour nous que nous soyons bien unis» [for the reason that there was between the throne and the Duke of Orléans only the Duke of Bourdeaux, a four-year baby]; «Il nous importe et il vous importe encore plus que, dans le cas où [le duc de Bordeaux] viendrait à manquer,
vous et les vôtres puissiez recueillir la succession sans difficultés, sans embarras.
Vous savez bien qu'il y a des gens qui rêvent de la branche d'Espagne, je ne les crois pas nombreux, mais prenez-y garde. Il faut vous entendre avec nous pour étouffer cela.
Moi je suis prêt à vous y aider de mon mieux. Je désire épargner à la France les déchirements que cela lui causerait» (cit. in Antonetti).
An extreme position might be for Charles X to claim Infante Carlos of Spain (of Carlist fame) as his legitimate heir, in spite of course of the Treaty of Utrecht. Charles X still has a grand daughter, Louise Marie d'Artois, who is conveniently close in age to Carlos' son Carlos de Montemolin. So marry them and he could claim the French succession by either hyper legitimist rules or by some kind of pragmatic sanction. So if someone wants to claim that the renounciations of Philip d'Anjou override French law then you could just junk it and go for a female succession, which puts the same person on the throne anyways.
In Spain King Ferdinand VII of Spain was at his third marriage in 1820, and he has no children; the heir presumptive was at that time the King's brother, the Infante Carlos Isidro, already married since 1816; the other King's brother, the Infante Francisco de Paula married in 1819, then before of the assassination of the Duke of Berry.
Now, admitted that Ferdinand VII and the Cortes decide to free from the constraints explained above one of Infants, who to choose?
The Crown of France was most important and prominent over the Spanish crown?
If yes, Carlos Isidro had to give up the rights to the throne of Spain and to be chosen for the throne of France?
The Infante Francisco de Paula becomes heir presumptive to the Crown of Spain?
Or the opposite?
But in the latter case there would still be a division between the Head of the House of Bourbon and the Crown of France.
Idem for the sons of Carlos Isidro...
And why choose a Spanish prince to the crown of France?
In France was occurring in the public opinion and in the ideas of the politicians the division between "Fundamental Laws of the Kingdom", related to the Ancien Régime, and the new democratic convictions, liberal, directed at the conversion of the constitutional monarchy on a model more similar to British parliamentary model, with a king who reigns but does not govern (under Louis XVIII, for example, the Chamber of Deputies proposed amending Salic law to allow the Duchess of Angoulême to accede to the throne:
Fundamental Laws of the Kingdom, Rest in Peace).
And then, in the 1820s Charles X has sixty years and the Duke of Angoulême not yet fifty, that is to say two possible reigns that will last at least another thirty years. The choice of an heir could still be postponed and, who knows, Charles X could procrastinate while waiting that events lead to a solution.
From the words spoken to the Duke of Orléans, mentioned above, and the choices made also in OTL during the July Revolution, it is understood that Charles X wanted to avoid civil war.
The choice of a Spanish prince, although freed from the King of Spain and by the Cortes of his unavailability, would not find acceptance in most of the public and politicians more democratic and liberal, on the contrary it would lend the side by Republicans and Bonapartists, seen as the only hope to avoid chaos and civil war.
Even for the supporters of a constitutional monarchy, democratic and liberal, the choice could only fall back, in any case, over the Duke of Orléans.
I therefore think that waiting to see how events were going waiting to choose an heir, Charles X would have behaved in the same way of OTL with the same results politicians.
A possible difference with the OTL is that on 31 July 1830 the liberal deputies with the aid of La Fayette have suppressed immediately the republican insurrection in Paris and they have proclaimed Louis-Philippe of Orléans not Lieutenant Général du Royaume but immediatly king.
No? Your opinions?