It is unclear from your question what do you mean by "separated from the state".
In fact European history knows only one theocratic state - the area under direct papal control centered in Rome, known at different periods as Papal states or Vatican.
The rulers of all other European states were secular persons.
Still the laws of many European states empathized Christianity as the state religion or Christian god as the source of power.
In all European states the church performed some duties that now viewed as the duty of state. For example, the registration of births and marriages. But among population of different confessions these duties were performed by different religious bodies. For example, births and marriages among Jews were registered by Jewish religious organizations.
I will list some events that may be relevant to your question.
In the years 1103 to 1075 there was a dispute between the Pope and some of European monarchs, notably, the Holy Roman Emperor over who has the right to appoint church officials such as bishops. Traditionally they were appointed by the emperors but the dispute led to the outcome that this power was limited.
This event can be seen as making local church hierarchy somewhat independent from the monarch.
The political struggle between sovereign monarchs and the church lasted for many centuries with monarchs either trying to limit the Church power, or to take control over church themselves as it happened in Britain and Russia.
In 1144 the population of Rome revolted in an attempt to establish a secular government, known as Roman Commune. The revolutionaries expelled Pope and declared allegiance to the Holy Roman Emperor.
As a result of Protestant reformation and the Thirty Years War it became impossible for many states to maintain allegiance to a single confession. In many countries the laws were modified so to reflect the multiconfessional character of the population. This mostly touched the Holy Roman Empire.
The Great French revolution of 1789–1799 was marked with boldly anti-Catholic character. Started with removing the church privileges and trying to subordinate the church to the state (as opposed to separate) by making all clergy the state employees it proceeded to an attempt to replace Christianity with some secular cults. This somehow followed the way of reforms by Peter the Great in Russia who abolished the patriarchal chair and made the Church essentially a state ministry by putting a secular ober-procurator in the head of the church.
Thomas Jefferson the United States in a private letter for the first time declared that the church should be separated from the state in 1802 but this declaration had no legal force. Still some US courts later cited this letter in the rulings.
France in 1905 declared the state separated from the church by law.
The Russian revolution of 1917 followed the case by declaring the church separated from the state, essentially rolling back the reforms by Peter I. The patriarchal chair was restored, and the state launched massive atheist propaganda.
It seems the first state declared officially atheist was Albania, where in 1977 production, distribution and storage of religious literature was made a criminal offense.
