The Church is officially neutral vis-a-vis the form of government or constitution to be adopted in a given country, so long as it upholds freedom of religion, natural rights, the basic well-being of its citizens etc.
Traditionally, nevertheless, the majority of Catholic theologians and political philosophers have favoured the “
mixed government” model. From the Summa of Saint Thomas Aquinas (1225–1274) :
newadvent.org/summa/2105.htm
Article 1. Whether the Old Law enjoined fitting precepts concerning rulers?
…
I answer that,
Two points are to be observed concerning the right ordering of rulers in a state or nation. One is that all should take some share in the government: for this form of constitution ensures peace among the people, commends itself to all, and is most enduring, as stated in Polit. ii, 6. The other point is to be observed in respect of the kinds of government, or the different ways in which the constitutions are established. For whereas these differ in kind, as the Philosopher states (Polit. iii, 5), nevertheless the first place is held by the “kingdom,” where the power of government is vested in one; and “aristocracy,” which signifies government by the best, where the power of government is vested in a few. Accordingly,
the best form of government is in a state or kingdom, where one is given the power to preside over all; while under him are others having governing powers: and yet a government of this kind is shared by all, both because all are eligible to govern, and because the rules are chosen by all. For this is the best form of polity, being partly kingdom, since there is one at the head of all; partly aristocracy, in so far as a number of persons are set in authority; partly democracy, i.e. government by the people, in so far as the rulers can be chosen from the people, and the people have the right to choose their rulers.
Such was the form of government established by the Divine Law. For Moses and his successors governed the people in such a way that each of them was ruler over all; so that there was a kind of kingdom. Moreover, seventy-two men were chosen, who were elders in virtue: for it is written (Deuteronomy 1:15): “I took out of your tribes wise and honorable, and appointed them rulers”: so that there was an element of aristocracy. But it was a democratical government in so far as the rulers were chosen from all the people; for it is written (Exodus 18:21): “Provide out of all the people wise [Vulgate: ‘able’] men,” etc.; and, again, in so far as they were chosen by the people; wherefore it is written (Deuteronomy 1:13): “Let me have from among you wise [Vulgate: ‘able’] men,” etc. Consequently it is evident that the ordering of the rulers was well provided for by the Law.
It should be noted that medieval scholars understood “democracy” in its classical Athenian variant.
Contemporary representative democracy - with its Anglo-Saxon/Montesquieu-like division of powers between executive [which retains kingship], judiciary [which retains an expert ‘aristocratic’/rule of the best element] and elected legislatures [fulfilling the requirement of ancient democracy], fits this model of ‘mixed’ government perfectly.
It is not surprising, therefore, that since Leo XIII and especially since the pontificate of Pius XII the church has favoured ‘representative democracy’, with John Paul II even commending it in one of his encyclicals.