I'm comparing Napoleon III to Bismark and their influence on Europe leading their respective countries however I'm struggling to think of arguments for Napoleon. I first thought I could argue Napoleon was integral in ultimately unifying Italy due to the Second Italian War of Independence but that argument seems to be weak when you look at the Third Italian War of Independence which was made possible by Prussia. It seems Napoleon played a fairly weak role in Europe been disappointed by not getting any territorial gains in guaranteeing neutrality in the Austro-Prussian and been diplomatically isolated by Bismark. Is there anything notable Napoleon III did in foreign policy that was successful after the Crimean War which was influential in Europe
While we can say that Napoleon III had serious political failures as you mentioned, he was the leader who aligned France as an ally of Great Britain -- something that continued to WW1, WW2, and even today. He also restored French prestige as a military power beyond what previous rulers accomplished. Not to mention territorial gains in Savoy and Nice, consolidation of Algeria.
In addition, one should not forget his various colonial ventures: Mexico, Indochina, the construction of the Suez Canal. While the French adventure in Mexico failed to achieve his goals, France did manage to keep Indochina well into the 20th century.
You may argue that Indochina had little impact on Europe, however the Suez canal did, and still do, today.
France did make two territorial gains during the Second Empire, the annexation of Nice and of Savoy in 1860 after the Treaty of Turin.
Overall though, Napoleon III was not very influential on a European scale. You mentioned his role in the Crimean War, which was arguably his greatest success as it returned France to the rank of "decision maker" after the humiliation of the Treaty of Vienna (something Napoleon was acutely aware of). But yeah, if you compare him to Bismark... He's sure to come up short :)
Napoleon's policies were a lot more effective inside France (where he pretty much single-handedly created the modern French rail network) and in the colonies (he brought the Algerian colony much closer to French public consciousness, strengthened French positions in West Africa, and participated in punitive expeditions against China with the UK, to whom he was allied).
There's a great book that I read a few years ago (unfortunately in French) that goes over the good and the bad of the Second Empire on both a domestic and foreign policy level, "Le Second Empire" by Pierre Miquel. Here it is on Amazon, really recommend it.
EDIT: If you want some information about the annexation of Nice in 1860, here's an article that goes into a bit more detail about how it happened. Incidentally, some of my family lives in Nice and I was there in 2010, when the city put on some celebrations and exhibitions to commemorate the 150th anniversary of the plebiscite.
If you look at the Franco-Prussian War, you could potentially see Bismark's successes as Napoleon's failures. So, in that sense, you could say that Napoleon III was influential insofar as threw his country into a unwinnable war with Prussia and from there, all you have to do is add up the results of France's defeat, two of which seem particularly important to your scope:
The defeat in 1871 and the humiliating armistice negotiations caused much resentment in France for decades. This burning sense of loss was dubbed "revanchisme" (revenge-ism) and certainly contributed to hostility which culminated in World War One.
Decades after the war, a famous trail dubbed the "Dreyfus affair" put a jewish French soldier on trial for treasonous acts supposedly committed during the war. The trial was obviously a scam, and Dreyfus (the soldier) was being used as a scapegoat for a lot of France's feelings of betrayal and shame - emotions that should really have been directed to Napoleon III or to actual traitors. Since Dreyfus was jewish, many of those who accused him did so in order to justify pervasive feelings of anti-semitism. The trial is often pointed to as one oft he first moments in modern history that anti-semitism reared its head in Europe. Europe is still dealing with a lot of the misconceptions and stereotypes that 19th century anti-semitism expressed itself in.
This might be a little different than what you were looking for, but frankly Napoleon III is not well known for his foreign policy. His economic policy is something else entirely!
One source that helps understand how Napoleon III and, more generally, France of the Second Empire was perceived by their contemporaries is Mark Twain's memoir "Innocents Abroad" [0].
"Innocents Abroad" tells the story of a tourist trip made by a group of Americans in 1867. They visited many countries in Europe (including France and what is now Germany) as well as the Middle East traveling mostly on a steamboat.
Mark Twain describes witnessing Napoleon III giving speech to the public during World Expo of 1867 [1] which he attended. He also writes in detail about his impressions of the french society and the state of the country in general and compares them both with the US and other places they get to visit.
It is an absolutely fascinating read and I recommend it to everyone. The tl;dr is that it shows that at the time France is perceived to be the well-established world leader in progress, industry and social change, somewhat similar to where we would put the United States today.
Mark Twain is amazed by how developed France appears to be: railroads working flawlessly, countryside looking wealthy, people appearing cultured and well-off.
His impressions of Napoleon is that he is an enlightened leader who stands for progress and liberty. He contrasts him to an Ottoman sultan who is also present during the Expo as a guest and his point is that the sultan is a despot and stands for the old world of brutality and misery and Napoleon III is the opposite of that.
That trip is, of course, before the war with Prussia.
I think it's a mistake to undervalue Napoleon III's contribution to the unification of Italy. While he wasn't really involved in the Third War, the Second War was pretty important and his support for the Kingdom of Sardinia paved the way for it to ascend to position as the Kingdom of Italy, even if another war was required to attain it. As a reward for this effort he received territorial gains in what is now southern France, a Nice accomplishment (that was a pun). As others have mentioned his role in creating a long term alignment between France and Great Britain should not be undervalued. He also oversaw a vast expansion of the French Colonial Empire.
Although not as flashy as his territorial gains, the economic programs of Napoleon III should also be mentioned. He lowered tariffs and reformed much of the French economy to make it more efficient and create closer economic ties to France's neighbors (notably Britain).
Finally Napoleon III played a pivotal role in many of the diplomatic issues that arose in Europe during his reign. Unfortunately that's a bit harder to discuss, because it's more nebulous.
I don't think I'd say Napoleon III was as influential as Bismark, largely because Bismark is a towering figure who reshaped European politics forever. That said Napoleon III did leave behind a fairly impressive legacy in Europe, much of which tends to be ignored in light of his diplomatic and military failures surrounding the Unification of Germany.
Sources: Napoleon the Third and his Carnvial Empire by John Bierman