The short answer to your question is yes: multiple foreign nations took interest in the events of the American Civil War. A full answer to this question, which I will attempt shortly, requires a more nuanced understanding of the historical phenomena that characterized economic and political thought in the 19th century. In the discussion below, I am largely drawing upon David Goldstein's America Aflame and James McPherson's Battle Cry of Freedom to describe the diplomatic relationships between the US (CSA) and Europe. For the discussion of the European political atmosphere I relied largely on Barbara Tuchman's Great War Series, which chronicles the diplomatic system that eventually gave way to WWI.

19th century diplomacy and technology catalyzed the development of the complex global markets and dynamic political community that govern world affairs today. Indeed, the world in the mid 19th century was not quite so disconnected as many believe, and it is likely that countries in Asia or even South America remained well informed regarding the events of the war. Regardless, in the 1860s US relations with non-European powers were mostly in their infancy. China opened its ports to the US in 1842 while Japan did so in 1854. I’m not familiar with any sources that discuss US wartime relations with Asia, but I’m inclined to believe that diplomatic relations with Asia at this time did not extend far beyond preliminary economic agreements (see: Treaty Ports) and a trickle of commodities trading. While Southern cotton certainly found its way into Japan and China, this incipient economic relationship did constitute the same level of foreign interest as did the United States’ more extensive commerce with Europe. Besides the historical timeline, this portion of my answer is largely conjecture and I invite any additional information that might nuance to this conclusion.

As I alluded to previously, US commerce with Europe at this time constituted one of the most profitable and robust commercial relationships of the time. By the mid 19th century the United States had begun to scratch the surface of its vast potential as an economic juggernaut. Though Northern industry did not truly take off until after the war, ports like Baltimore and New York remain significant in the antebellum period for the sheer volume of commerce that went through their harbors. This New York Times Article provides information and statistics on the foreign trade that took place in these parts. However, the discussion of wartime economics and foreign relations inevitably centers on the agricultural exports of the South. During this time, Southern agricultural products accounted for something like sixty percent of US exports. History has thoroughly documented Britain’s dependence on US cotton for its Northern textile mills, yet France occupied a similar economic position. The Union blockade of Confederate ports during the war incited a cotton famine that affected industry in both countries. From a purely economic stance, both Britain and France had a vested interest in a Confederate victory that would allow the cotton trade to continue, unfettered by federal military intervention or economic regulation.

Just as economic conditions compelled French and British interest in the war, the political realities of the time brought the war to the attention of the Russian Empire. The great powers of Post-Napoleonic Europe played a precarious political game that focused on a balance of power throughout the continent. Fragile systems of alliances managed to evade large, continental wars, but did little to mitigate divisive political jockeying. Britain and France had no alliance, but they shared two distinct interests at the outbreak of the war: Southern cotton, and a desire to curb the growing power of Prussia and Russia. For Russia, a Confederate victory would mean added might for its prospective enemies in Britain and France. With such an ingrained economic relationship, the CSA would undoubtedly seek out an alliance with the two western powers. The Tsar championed the preservation of the American union, hoping that a victorious federal government would prove a strong ally against Britain and France. Importantly, Russian support during the war was strictly verbal, though the Russian fleet did dock in New York and San Francisco in 1863 (the Czar claimed his fleet was not safe from Polish Nationals while anchored in the Baltic).

Though the three great powers of the time did take an interest in the war, support remained tend and the three countries ultimately remained essentially neutral. This disconnect between theoretical and practical had mostly to do with contemporary intellectual trends and historical circumstances. The famous - and failed - revolutions of 1848 unleashed a rising tide of liberalism across the continent. Liberal though spread rapidly through France, where public political sentiment ran completely counter to the idea of an independent planter oligarchy. Britain was slightly more insulated from the throes of of continental upheaval, yet they shared the French disdain for slavery. Britain outlawed the slave trade in 1808, and could not justify supporting Confederate institutions after 1863, when the Emancipation Proclamation made clear that the fight was for the existence of slavery.

During the American Civil War, Mexico was involved in its own civil war between liberals lead by Benito Juarez, and Conservatives Lad by Maximilian I and backed by French forces sent in by Napoleon III. Napoleon's plan was to set up a puppet kingdom in Mexico and through there send supplies and arms to the Confederacy in an attempt to stop the U.S. from growing too powerful. Unfortunately for him, Mexican Liberal forces controlled two thirds of the country including the entire border with the United States and the conservatives were eventually defeated. The Mexican government didn't meddle directly in the American Civil war, but it did profit from it. The United States quickly moved to take over the port of Brownsville at the mouth of the Rio Grande to keep cotton from going out. Entrepreneurs like Richard King and Mifflin Kennedy would then have mule trains take the cotton upriver and away from Union controlled areas, then cross it over to the Mexican side and load it into boats they registered in Mexico. After that it was just a matter of floating your boats down river on the Mexican side, within full view of the Union forces and sail to the port of Bagdad across the river from Brownsville. From there it was stored, or sailed out to waiting boats from various European Nations. Mexico of course collected a tax on the whole thing so there was no incentive to stop them.

Apologies for this late answer, but Stephen Platt's Autumn in the Heavenly Kingdom (2012) makes the interesting suggestion that Britain needed to force a quick resolution to either the US Civil War or the Taiping Rebellion (the latter entering its endgame as the US Civil War started). The reasoning is that the US Civil War had disrupted British imports of Southern raw materials like cotton and the export of finished goods like textiles back to America, whilst the Taiping Rebellion so destabilised the position in the Yangtze basin that trade became unsafe both up and downriver, placing Britain on the cusp of an economic crisis that required one of these wars to be resolved quickly. The British government saw fewer moral qualms (and perhaps a far easier time) with intervention in China and so intervened there.