You're probably thinking of Geneva, which was governed by a protestant Grand Council, with John Calvin actually present as the city's spiritual leader between 1536 and 1564. This predates 'Calvinism' as it would be spoken of today.

Other cases include the English Commonwealth (and Protectorate directly under Oliver Cromwell) from 1649-1660, which contained a hodgepodge of Puritan thought, with some strong Calvinism. This government affirmed the Westminster Confession of Faith of 1647, which remains the typical Reformed confession for the Anglophonic world.

That theology and the political theory it implied would extend to some of the British colonies in North America, which grew after the restoration of the English monarchy through the emigration of religious dissenters. One could make a semi-elastic claim that the United States is the only enduring nation founded by Calvinists.

There were a lot of states inside the Holy Roman Empire which followed the reformed "confession", mainly based on the Heidelberg catechism (1563) which in turn was based on the reformed catechism of Geneva. Most notable was of course the Palatinate where Heidelberg is located. Other notable reformed states and cities included: The city of Bremen, the county of Isenburg, the county of Limburg, the county of Lippe(-Westphalia), three of the five counties of the house of Nassau, the counties of Wied and of Wittgenstein.

These were mostly smaller states, but the fact that one of the imperial electors followed the Calvinist beliefs ensured them the recognotion in the peace treaty of 1648.

This peace treaty mandated that the religious adherence should always stay the same, meaning that a prince couldn't convert his people after he acquired new land. This lead to a unification movement in the 18th and 19th century. Lutheran and Reformed church were merged to a united church.

I remember hearing one founded on it in early Europe while I was in high school, but I can't find a link to the name of it.

You might have mixed up something. There was only one attempt to form a baptist society. The "Täuferreich von Münster" (in English called "Münster rebellion) ended up badly, its leader Melchior Hoffman tried to build the "New Jerusalem", but was suppressed violently with the consent of both Lutherans and Catholics. The introduction of polygamy under Hoffman's leadership caused a huge scandal back in the day.