I'm asking this question because I learned the Prussian army was back then already disciplined and modern. Wilson intervened 35 years later against this same army.
I realize the German Unification was one step in a longer process but was there a sense of foresight in the US about a new confrontation between France and Germany? How did the US feel at the end of the 19th century about Germany potentially dominating Europe?
In the 19th century, the average American was rather distant from European affairs and likely couldn't imagine America involved in any real wars with a European power. The American Government, on the other hand, definitely could see a conflict coming over Latin America.
The Monroe Doctrine, issued in 1825, called for no further interference in Central and South America by European countries outside of their already established colonies. Interference would be viewed by the United States as an act of aggression. The doctrine was initially anti-colonialist, but was used to justify an awful lot of imperialism by the United States by the end of the 19th century, as in the case of Hawai'i and Cuba. Other countries were obviously under no obligation to follow the whims of the United States, though many did as the power and navy of the US grew. Great Britain was a proponent of the Monroe Doctrine from the beginning because it also furthered their aims of keeping the rest of Europe in a weaker position, colonially speaking.
Thus, when the Second French Empire under Napoleon III invaded and overthrew the President of Mexico in 1862, they were viewed as an aggressive colonial power by the United States, and interfering in America's sphere of influence. France had Mexico set up as the Second Mexican Empire ruled by an Austrian noble named Maximilian. The United States was, of course, tied up in the American Civil War in 1862 and could do little but make a lot of noise about the whole affair.
In 1865 when the American Civil War ended, American interests turned to Mexico which was slowly imploding due to poor rule under Maximilian. France withdrew their forces rather than face a war with the United States over a failing state, and the Mexican Empire collapsed. This was all set against the backdrop of the French Empire briefly considered intervening in the American Civil War on the side of the Confederacy in 1861-62. This included some unofficial meetings between the French Emperor and Confederates, but nothing official ever came of it since Great Britain refused to take sides. By 1871 the French Empire and the United States were on unfriendly terms.
So how did America view a unified Germany? Germany and America didn't have a lot of interaction prior to unification in 1871, outside of trade, as both were rather inward looking societies. Direct colonialism and imperialism weren't priorities for America and the German states during the middle 19th century.
German-American immigration was huge during the 19th century. Over six million Germans immigrated to the United States during that time, especially to urban areas in the North, as well as the American midwest and Texas. Some cities in the midwest like Omaha and Milwaukee were actually made up primarily by first and second generation Germans. German-Americans were strongly against slavery, and hundreds of thousands volunteered to fight for the Union. Nearly 200,000 Union soldiers were actually born in Germany! German was the second most spoken language in the United States from the late 1700's until the early 20th century.
At the same time, in the German states, the United States was viewed as a land of prosperity. Tales of rich uncles in America were popular tropes in German books and short stories. Many people followed the events of the war through papers and calendars and were almost universally pro-Union. Otto von Bismarck even later viewed the German wars of Unification as a kind of parallel to the American Civil War, and was an admirer of Lincoln. America did not have a particular stance on Germany, but due to the huge German population, and relations with France, there was no negative view on Germany.
With the Franco-Prussian war concluded, German-Americans celebrated in the street and French-American's, who were outnumbered approximately 10-1 by German-Americans, wept. The American public was largely indifferent to the events in Europe, and the American government was happy to see an imperialist France cut down a notch.
As the 1870's rolled by Germany continued to be viewed favorably in the US. They did not partake in much further imperialism or land grabbing and appeared to be pushing for peaceful internal growth. President Grant became close with Bismarck. Germany was, despite being an Empire, also rather democratic for the time.
In the 1880's and 1890's Germany was becoming the cultural and political center of Europe, and they sought to flex their power more. Their greatly expanded navy brought them into conflict with Great Brittian, and attempts at colonial expansion in the Caribbean and the Pacific strained relations with the United States.
With the removal of Bismarck's guiding hand in 1890, Germany and American relations nearly came to a boiling point several times. The Monroe Doctrine was basically disregarded by Germany. War nearly broke out between the two powers over the Panama Canal, the Venezuela Crisis, and a planned intervention in Mexico in 1911 by Germany.
While France was viewed unfavorably in 1871, the hatred was more directed at Napoleon III than France itself. With his removal from power relations quickly returned to friendly between the two old friends. The reinstatement of the French Republic secured France a special place in the heart of Americans as France was the only true republic in the Europe. Similar to the Germans, the French people idolized the United States as a land of promise. The Statue of Liberty best symbolizes the relationship between the two countries in the late 19th century.
German attempts to generate conflict between France and the United Kingdom usually saw America siding diplomatically with the French and UK instead of Germany, as happened in Morocco in 1906 and 1911 during the first and second Moroccan crises. French colonialism rarely conflicted with American colonialism in the 19th century. France had long established colonies, while both American and Germany were late to the game and fighting over the left overs. Germany, post-Bismarck, was also antagonistic towards the other European powers in an attempt to gain more power. American supported a balanced and peaceful Europe as it was good for her interests.
By the time the First World War broke out America was neutral but clearly a friend of Great Britain and France. In the early 20th century American had come close to conflict with Germany several times, but did not imagine they would be involved in a major war with Germany in Europe.
Philip Sheridan at his request, was dispatched by President Grant as a military observer of the Franco-Prussian war, and was there when Napoleon III surrendered at Versailles. Interestingly Sheridan was unimpressed with the German way of war:
From his memoirs here
"Following the operations of the German armies from the battle of Gravelotte to the siege of Paris, I may, in conclusion, say that I saw no new military principles developed, whether of strategy or grand tactics, the movements of the different armies and corps being dictated and governed by the same general laws that have so long obtained, simplicity of combination and manoeuvre, and the concentration of a numerically superior force at the vital point.
This is certainly an interesting conclusion: the German General Staff system was world class. It would be interesting to explore more deeply why Sheridan didn't think much of it.