Not a historian, but I'll offer an answer. The foreign (particularly European) perception of the US obviously varied quite widely during different times in the 19th century. In the early 19th century circa-War of 1812, the US was certainly not a comparable power to France or Great Britain. Still, there was never really a chance of returning the US to colonial status given that it had nearly doubled in size after the revolution. Here is an /r/askhistorians post I asked a while back that has more details on this.

By the 1820s, the Monroe Doctrine had begun the principle that it was in the US interest to enforce the independence of the western hemisphere from further European intervention. This was certainly an important precursor to the US being the hegemon of the western hemisphere, but at the time it didn't really have the military capacity to enforce such a doctrine on its own. This certainly would have signaled to European powers that they wouldn't have to worry about the US intervening in their affairs (not that they really had the capacity to anyway). By this time the British, specifically Foreign Secretary George Canning, acknowledged the US to be the leading power in the American continents, but the British had to take it upon themselves to actually enforce the Monroe Doctrine with their naval power, given their interest in keeping other European powers from expanding their sphere of influence in the western hemisphere and threatening British trade.[1]

By the 1840s, Mexico had become independent as well as other Latin American countries, but the US was clearly capable of dominating them militarily, as evidenced by the Mexican-American War. The US was becoming a continental power which greatly increased its economic capabilities. By the time of the Civil War, the US was also industrializing and building significant railroad infrastructure. It was able to effectively enforce the Monroe Doctrine as well, as it was able to use the threat of war to force French withdrawal from Mexico that had occurred during the Civil War. [2]

The Civil War was definitely a major turning point for the US as a nation-state. It was more centralized politically after that time, and was able to demonstrate its capabilities to wage large-scale modern warfare. It was able to focus on broader economic development and industrialization afterward, which a few decades later would put it on par with Great Britain as an industrial power.

The final decades of the 19th century saw the US even establishing its own colonies in the Pacific and Caribbean. It was able to handily beat Spain, a former colonial power, in a short war. It was also regularly intervening in East Asia along with other European powers - such forcibly opening Japan and Korea to international trade - and intervening in China. And it was attracting thousands of immigrants from Europe.

So America's international prestige by the end of the 19th century was worlds away from the way it was at the beginning. It could definitely be considered a great power by that time, even if it still was not superior to powers like France or Great Britain.

[1] H. W. V. Temperley. "The Later American Policy of George Canning". The American Historical Review. Vol. 11, No. 4, Jul., 1906. Pg 779-797 http://www.jstor.org/stable/1832228

[2] Manning, William R.; James Morton Callahan, John H. Latané, Philip Brown, JamesL. Slayden, Joseph Wheless and James Brown Scott (25 April 1914). "Statements, Interpretations, and Applications of the Monroe Doctrine and of More or Less Allied Doctrines". American Society of International Law 8: 105 http://www.jstor.org/stable/25656497

[Keep in mind, this is my first time answering a question and it might lack depth. Also, I am a history FAN not an actual historian. Feel free to take my answer with a grain of salt.]

European powers, especially the British, did not see America as a force to be reckoned with. This is part of the reason we see the War of 1812 develop. It is basically a war that breaks over the British not respecting American sovereignty. One of the main reasons for this war was British impressment of American sailors. Without proper authority, the British would board American naval vessels under the pretext of "We're looking for British deserters". At the time, the British were fighting Napoleon and needed all the sailors they could get, hence the reason for boarding American ships. At the time, there was no proper identification for Americans so the British actually never knew if the person they were taking was an actual British citizen as old British sailors would tattoo eagles and American flags on them to blend in. To American politicians like Jefferson and Madison, this was blatant kidnapping of American citizens. This impressment is a great example of how post-Revolutionary tensions made the British think very less of Americans. Britain would not do this to other nations like Prussia or Russia or France because there was a real chance for a full out, bloody war.

In fairness to the British though, American politicians were very aggressive in their DESIRE for war against the British. Americans believed that the British were supplying Native American raids and armies (which they most likely were) and the Americans were eyeing Canada to expand their territory.

But I digress from the War of 1812 as that does not define the entire 19th century, twas only the beginning. Much like the Roman Republic, America could not be powerful enough to efficiently fight distant powers until it dealt with those at its gates. The wars against the Seminoles (and many, many other tribes) were representative of the Roman wars against the Gauls of the Po Valley. The Civil War which saw a professionalization and deadly increase in efficiency of the army would be like the Social War against traditional Italian values. In that case, we compare Lincoln or Grant to Sulla for the use of such a military force to unite the peoples of the same land under a similar ideal. Mexico would be America's Carthage and with the utter defeat of Mexico, the elimination of non-Indian rivals in America was complete. With these wars after the War of 1812 (which we may compare to the Gallic sack of Rome in 390 BC), America was set to expand in its on backyard without the threat of European incursions. Without extremely powerful and disciplined armies to resist them, the American military can be thought as a powerful world power after the American Civil War or about the 1870's when territorial expansion was inevitable. Don't disregard the fact though that America had been a world power after their kind of-victory in the War of 1812 but it was still seen as inferior to the armies of Europe. But in the mid or late-19th century, we see America as force to reckoned with. The same force that would defeat the Spanish in 1898, crush the Filipino revolts, hold the Argonne in 1918. It is after the late-19th century that we see America go from this isolationist, divided power to a unified, militarized state that could compete with almost any European power. So to answer your question, originally no but eventually yes.

[Keep the original warning in mind, please. Thanks and hoped this helped]