Why "French Republic" and not "Republic of France"?

Factual Questions
1

AFAICT, the most common form for country names is (government) of (country), not (adjective) (government). The exceptions are as follows:

Argentine Republic (República Argentina)
Central African Republic (Republique centrafricaine)
Czech Republic (Ceska Republika)
Dominican Republic (República Dominicana)
French Republic (République française)
Gabonese Republic (République gabonaise)
Hellenic Republic (Elliniki Dhimokratia)
Italian Republic (Repubblica Italiana)
Kyrgyz Republic (Kyrgyz Respublikasy)
Lao People’s Democratic Republic (Sathalanalat Paxathipatai Paxaxon Lao)
Lebanese Republic (Al Jumhuriyah al Lubnaniyah)
Great Socialist People’s Libyan Arab Jamahiriya (Al Jumahiriyah al Arabiyah al Libiyah ash Shabiyah al Ishtirakiyah al Uzma)
United Mexican States (Estados Unidos Mexicanos)
Portuguese Republic (Republica Portuguesa)
Russian Federation (Rossiyskaya Federatsiya)
Slovak Republic (Slovenska Republika)
Swiss Confederation (Confederation Suisse, etc.)
Syrian Arab Republic (Al Jumhuriyah al Arabiyah as Suriyah)
Togolese Republic (République togolaise)
Tunisian Republic (Al Jumhuriyah at Tunisiyah)
United Arab Emirates (Al Imarat al Arabiyah al Muttahidah)

Now I notice that many of the European republics are of this form, with the noticeable absence of the Federal Republic of Germany and the Republic of Finland; interestingly, we have the Kingdom of Belgium, even though it is ruled by the King of the Belgians.

However, nearly all colonial republics are “of”; Republic of Ecuador, not Ecuadorian Republic, and so forth.

Speculation as to why this might be?

2

The Republic of Ireland is another European exception.

3

I suspect that in many cases it’s a translation of the name in the country’s language, and that language allows one form and not the other. For example, I think French requires “la République française” and not “la République de la France” – the first is certainly far more common when you do a Google search. On the other hand, a literal translation of “Bundesrepublik Deutschland” would be “Federal-Republic Germany”, which is not good grammar in English, so it becomes “Federal Republic of Germany” – though “German Federal Republic” would also be fine in English.

4

Speculation only: European peoples had collective names before the nation itself received a name; in short the “Francs” (as a name) existed before the name of the nation “France”. Thus it seems more likely that the government would be described as “French” rather than “of France”.

When new areas were colonized, it was natural to name the land first and the inhabitants second (if at all). Furthermore, if a government was organized, it was first organized by colonists who still saw themselves as part of the original collective name; Spaniards (not “Ecuadorians”) set up the initial government in the area that would become Ecuador. Again, as the land was named first, and the original colonists identified themselves with their homeland collective rather than the native population, I think it would be natural to call e.g. the Spanish government in Ecuador the “Republic of Ecuador” rather than the “Ecuadorian Republic”.

5

Part of the reason is that you are wrongly imposing English grammar on other languages. The “Repubilc of X” vs. “X-ian Republic” distinction is one which does not exist in many languages. Hungarian, for example, doesn’t even have a word for “of”, so the only natural way of representing “Republic of Hungary”, Magyar Köztársaság, literally translates to “Hungarian Republic”. I suspect the same is true of Finnish and other highly inflected or agglutinative languages.

6

Turns out that “Magyarország” gets over 10 times as many Google hits as “Magyar Köztársaság”. All the hits of the latter, if my sight-reading of Hungarian can be trusted, use the phrase specifically in reference to governmental or administrative functions of the state. The official name of the country itself is of course Magyarország.

That would be “Suomen Tasavalta”, using the genitive case of Suomi, Finland. However, the official name of the country, Suomi how i love ya how i love ya got nearly three thousand times as many Google hits.

Turkey is different, because the official name is Türkiye Cumhuriyeti, literally ‘Republic of Turkey’, using the third-person possessive pronominal suffix. However, everybody when speaking unofficially just calls the country Türkiye. I googled and found that Türkiye gets about 9 times as many hits as the official name Türkiye Cumhuriyeti. The alternative form from the OP would be Türk Cumhuriyet, literally ‘Turkish Republic’, but it got less than 1% of hits compared to the others, some hits only incidental coocurrences of the word, not used as a phrase except in the case of misspellings of the Turkish Republic of Northern Cyprus, Kuzey Kıbrıs Türk Cumhuriyeti — in this case the word for republic gets the possessive suffix -i again to link it with “Northern Cyprus”, with the same function as the English word ‘of’, as psychonaut noted.

The name of the old Ottoman state was Devlet-i Osmaniye-yi Âliye, ‘the sublime Ottoman state’, using a Turkicized form of Arabic words strung together using Persian syntax. A very non-European model, that.

The official name of Mongolia follows the adjective+noun pattern: Mongol Uls, literally ‘the Mongolian nation’. Uls can be translated ‘country, nation, state’, take your pick. The way to say republic in Mongolian is bügd nairamdakh; as it turns out, Bügd Nairamdakh Mongol is the title of the Mongolian National Anthem, not the name of the country. Like I always say, “go figure.”

7

That will be news to the Hungarians, then. Both the CIA World Factbook and my Hungarian passport list the full name of the country as Magyar Köztársaság (“Republic of Hungary”). I could dig out my birth certificate but I’m pretty sure it will say the same thing. Magyarország (“Hungary”) is simply the short form, and could just as easily refer to Hungary as a republic as as a kingdom (as it once was).

8

Oh, the short form. You’re right, I should have checked the short and long forms first. The Factbook is pretty handy for looking that sort of information up.

Sitting up on a Himalayan mountain, waiting for a yeti, getting impatient…

9

But then there would be a distinction, as was evinced in the example of the Republic of Finland, between using a genitive case of the noun “Finland” and the adjective demonym “Finnish”. In Latin, the distinction would be between “romanus” (“Roman”) and “Romae” (“of Rome”).

10

Don’t forget the Republic of Austria, the Republic of Bosnia and Herzegovina, the dissolved Federal Republic of Yugoslavia (now the State Union of Serbia and Montenegro, consisting of the Republic of Serbia and the Republic of Montenegro, the Principality of Liechtenstein, the Principality of Monaco, the Principality of Andorra, the Republic of San Marino, the State of the City of Vatican, the Kingdom of the Netherlands, thje Kingdom of Norway, the Kingdom of Sweden, thje Republic of Iceland, the Kingdom of Denmark, the Republic of Bulgaria, the Republic of Croatia, the Grand Duchy of Luxemburg, and others. I don’t think there’s enough of a rule here to discuss possible reasons for this alleged discrepancy between European and formerly colonial republics.

11

But I’d like to add something to the issue of Germany. Styling a political entity as “… of Germany” is a relatively recent phenomenon. In the middle ages, there used to be the Holy Roman Empire of German Nation. After the defeat of Napoleon, who had brought this to and end, the German Confederation (Deutscher Bund) was formed. In 1871, the German states were merged into the German Empire Deutsches Reich), which continued to be the official style until 1945. In 1949, the Soviet occupation zone adopted the name of German Democratic Republic and the West the name of Federal Republic of Germany. The latter was originally meant as a temporary entity which was about to be replaced with something new after reunification - German Republic or even Reich were dismissed as sounding too “final.” When reunification finally came in 1990 (surprisingly - since the 1950s, hardly anybody in the West would have thought this would be realistically possible), the East joined the West, espanding the style of Federal Republic of Germany to the Eastern parts as well.