PC: United Kingdom of France and Spain

[FouDuRoy]

The dearth of Bourbons in the 1880s does not have too much to do with the “bad 18th century“ in France (this was not a particularly bad century for Frenchmen anyway, since the French territory then had one of its longest streaks without any major wars fought on it, and economic growth was quite good) — the mortality rate during the 18th century is quite at par with other dynasties (Spanish Hapsburgs, Medici, Bavarian Wittelsbach etc. went extinct during that century); even though the Révolution itself did remove one Bourbon heir (Louis Capet's son), Marie-Antoinette was 37 when guillotined and so somewhat unlikely to make many more heirs (the previous queen, Marie Leszczynka, had her last (and tenth!) child at 34).

I do not agree.
The heir you are talking about is Louis-Charles (aka Louis XVII).
You seem to forget his cousin Charles-Ferdinand was assassinated by a Bonapartist. No French Revolution means no Bonapartism and no assassination. Also, Charles-Ferdinand would've likely married sooner than in OTL, had him not lived half of his life in exile.
And Louis-Antoine (aka Louis XIX) would not have married Marie-Thérèse. It is pretty unclear if the fertility issue came from him or from her so he may or may not manage to father a son with another wife.
Without the French Revolution, I think the eldest Bourbon branch is highly unlikely to die out.

But assuming the eldest branch still die out despite any likelihood (after all, there are the precedents of both Philip IV's line and Henry II's line), there would be a succession crisis. The validity of Philip V's renunciation was always disputed.
Louis XIV himself wrote to the British nobody in France would ever see this renunciation as valid (he was wrong about that: many people in France see it as valid).
When the Parliamant of Paris registered this renunciation, many parliamentarians did not dare to come to the session out of fear to be accused of high treason if Philip V or one of his sons finally became king of France.
Even the French revolutionnaires, when they wrote a constitution for a constitutional royalty in 1789, stipulated they did not presume anything about the validity of the renunciations in the royal family.
What is sure is that there would be no personal union between France and Spain. Such a thing was always out of question. Charles II's will was very clear about that. A descendant of Philip V becoming king of France, maybe, but not the king of Spain himself (or he would need to abdicate the throne of Spain and pass it to another relative).

Apart from anything else, that would provide a precedent to throw all the rest of the Peace of Utrecht -- in so far as any of its clauses hadn't been voided by later events, which Britain's possession of Gibraltar hadn't -- into question.

The Treaty of Utrecht also stipulated Quebec would stay a French colony. We know how much this point was respected on the long term.

If it were a stronger country, or an earlier point of divergence, it could, perhaps, happen.

In 1883? Too late. The French would laugh at the idea of pathetically weak Spain trying to force her claim to the French throne. At best, they would politely say no. They would then proceed to mobilize their army and navy, as well as fortify the Pyrenees, and crush the Spanish forces, if the Spanish tried to force the claim anyway.

The United States is likely to decide that this is an excellent opportunity to remember that they had an alliance with France and try to seize Cuba, their long-cherished ambition. This war will go very badly for Spain and very well for France.

Of course, it is very likely that the French will decide that the best way to avoid these kinds of problems is to proclaim a Republic. (Ironically, the Spanish had tried the same thing in 1873, when they were unable to decide who was the best contender to succeed Amadeo of Savoy.)

And this is before considering whether the Spanish Bourbons would actually have a claim to the throne or not.

Obviously, the only way the "Spanish Bourbons" could get the throne of France is not an invasion of France by Spain but a political victory of the French legitimists who, as a result, would simply offer them the throne of France.

The Bourbons circumvented this treaty by claiming that the blood of their lineage is superior to treaties.
This is what Philip did after the death of Louis XIV and that is why we still have a Spanish pretender to the French throne.

It is less a matter of blood than a matter of laws and a matter of conception of what French royalty is.
Actually, it is not the first time a treaty tried to change French succession laws. Long before that, there was the Treaty of Troyes. We know how this story ended. At this time, Charles VII's supporters developped the idea that the throne of France does not belong to the king and is a duty, not a right, for the princes, implying nobody can change anything to the succession order. This is called "Principe d'Indisponibilité de la Couronne" and it is part of the "Lois Fondamentales du Royaume de France".

I don't think the treaty of Utrecht was too big of a concern. Treaties can be changed. The bigger problem for the Spanish Bourbons to take the French throne was simply that they were regarded as foreigners by this time.

You are right.
This is the Orleanists' main argument. They are clever enough to realize that, from a political point of view, they can't base their claim on renunciations that the British extorted by violence and included in a treaty that even them do not respect (once again, the Quebec thing).
However, the "Spanish Bourbons" being foreigners is actually quite disputable. Several years ago, a Spanish guy I worked with told to me the Bourbons had nothing to do on the throne of Spain... because of them being French. I personally think they are at least as Spanish as Charles V and as French as Henry IV.