Maybe it's a stupid question, but a lot of Russian and Romanian writers and composers emigrated to France and/or wrote almost exclusively in French. Why France and not, e.g., Italy?
I am not so sure the reason in all of Eastern Europe, but I can shed some light on Poland. There were decent relations between Poland and France before the French Revolution, but it became much stronger at the start of the Revolution. Poland was partitioned by the Habsburgs, Prussia, and Russia in the 1770s, but there were revolts that began in the late 1780s, which France saw as a sister movement and lent support to. France even gave citizenship to Tadeusz Kosciuszko, who was a resistance leader in Poland. The independence movements in Poland used a lot of French Revolution symbols like the tricolor, copycats of the Jacobin Club, and even translations of the Marseillaise.
The improved relations between France and Poland continued during the reign of Napoleon and after. Napoleon was interested in reviving Poland and forced Czar Alexander to recognize the Duchy of Warsaw in the Treaty of Tilsit. The Duchy of Warsaw used the French legal system, Constitution, and serfdom was abolished. Napoleon also had a Polish mistress and son with Marie Walewska. Napoleon was a hero in Poland for a long time and France lent support to Poland in 1918 after it claimed independence.
Sources:
The Oxford History of the French Revolution by William Doyle
Napoleon: A Political Life by Steven Englund
I am not a historian but maybe I can help a bit with context.
Romanian is a latin language - very similar to french - which established a degree of closeness.
During the 1800's France was a leader among Europe, culturally, industrially and economically. It was also one of the largest countries by population. Around 44 million during the times of Napoleon.
In 1948 there was a series of revolution all over continental Europe which started with France and quickly spread to other areas. While not all of the revolutions were successful - it established France as a leader to follow.
You asked why not other countries. Italy itself was not a well established country until 1870. For a long time it was series of small independent states - or areas of land controlled by the Vatican or by the Austrians.
Germany was not a unified country either - and while Prussia was a power at the time - it was not as influential as France.
Also keep in mind that Eastern Europe is at the intersection of 3 empires: The Russian, The Ottoman and the Austrian, and for very long stretches of time - those people fought for independence and self governance.