citing a few points from Hagen Schulze's _Kleine Deutsche Geschichte_ (München, 1996):

The German-Danish War (1864) saw the first time the peripheral great powers did not meddle in German wars. This is traced to the Crimean War (1853-56), which resulted in: "Rußland und England tief miteinander verfeindet und zu einem Zusammenspiel auf dem Kontinent vorübergehend nicht fähig waren". (118) [Russia and England deeply antagonistic and temporarily incapable of cooperation on the continent.]

Schulze also explains that the Franco-Prussian war was begun by Bismarck (the powerful Prussian minister) using a minor diplomatic kerfuffle as a pre-text. In 1870, the Spanish throne was empty and it was offered to a Hohenzollern noble. France objected because of their fears of being surrounded by hostile forces. Bismarck saw that "Frankrreich isoliert dastand; England und Rußland zeigten sich desinteressiert" (119) [France stood isolated; England and Russia indicated their indifference.] Bismarck provided the famous 'Ems Dispatch' to the press, which created a diplomatic defeat for France. Because of Napoleon III's domestic situation, he was forced by this defeat to declare war without considering allies or external foreign support for his side. (120).

Schulze's comments explain the Crimean war as the reason for the great powers' non-interference in the Danish War. It is unclear if that reason still held in 1870. Or if in 1870, England & Russia were indifferent because the spanish throne appeared to them an insignificant matter & because Napoleon III rushed into war without discussion with other powers.

On the French side, Thiers actually tried to convince other great powers to help France. They all declined. Napoleon III was a fine politician, but his foreign diplomacy was quite frankly erratic. Let's try to see which countries could have helped France :

-Russia : the emperor Alexander II wasn't an enemy of France, and Thiers expected a lot. He knew many Russians hated the German minority within the Russian empire. But the tsar had good relations with Prussia at that time, France and the UK had stopped Russia years prior during the Crimean war. He saw no reason to fight in that war. After that, Russia had pretty good relationship with Germany, and became its ally in 1873 but was quite clear, when Bismarck implied a preventive war with France was possible, they would not tolerate such thing. Bismarck understood how crutial it was for Germany to maintain good relations with the Russians.

Austria-Hungary : they thought about it, after all, they had been defeated by Prussia three years before. But many things prevented them from doing it. They were recovering from a defeat but also from a total change of government. The dual monarchy was a new thing, a last attempt to save the Habsburg empire. With new institutions, it would have been risky to go to war. And when Austria was at war with Prussia, Napoleon III was negotiating with Bismarck to obtain some territorial compensations. France didn't move when Austria was at war with Prussia, why should Austria-Hungary help France? Besides, after just two months, Napoleon III was captured and it was clear that France had already lost. If the war had been more contested, maybe Austria-Hungary could have been convinced to join the French side, but France was quickly defeated as Austria had been.

Italy : it's true France had helped Italy in its unification process. But Italy at that time was a new country with a pretty weak army, they wouldn't have been to efficient against the Prussians. Besides, the relations between the two countries weren't at their best. Napoleon III wanted the support of the French catholics and sent troops to prevent Italy from annexing Rome. Obviously, such a move only made Italians very mad. Garibaldi still went in France with an army of volunteers, but that's about it.

The United Kingdom : Napoleon III had pretty good relations with the British. But this is nowhere near enough to erase years of enmity with France. The British were quite pleased to see France finally put in its place. After all, the French had declared the war, and the French were defeated, they had it coming for being overconfident. The elites, of course, were more reserved since the birth of a strong new country could completely change the balance of powers. But even if the UK was willing to side with the French their land army was way too small to matter in such conflict. It would have been a long economic war that no one would have wanted in the UK, especially if it was for the French.

So all in all, the French failed to gather support because : 1-they were the ones who declared the war. They learned from that mistake by making sure to let the Germans declare it during WW1. 2-Napoleon III made many mistakes and managed to alienate every potential ally. 3-France was quickly defeated, even if the war continued, everyone realised it was a lost cause.