First thread! I've searched a bit on here for alternate Franco Prussian timelines, but none of them involve a POD after the Battle of Sedan on September 2, 1870. Can you make the French Republic win this one? Victory is defined as any peace that does not involve loss of land, payment of indemnity, change of government, or withdrawal of overseas troops by France. Prussia can still form the German Empire, just preferably not in Versailles Palace
In an alternate timeline, just about anything is possible, but with certain butterflies that would have to be set into motion.
In reality, there was no way the French could defeat the Prussians, especially once the south German states joined in. The only plausble way this could be changed is if Napoleon III saw the trap Bismarck was laying for him with the Ems Telegram, and managed to persuade the majority of the French people that Bismarck was goading them into a war, and that they could be the better men by not giving Bismarck what he wanted.
Assuming for the moment that Napoleon III was successful, however, would not prevent Bismarck from forging ahead with his plans. He would be forced to improvise, possibly using the Zollverein as the basis for achieving his political goal. Meantime, Napoleon III could convince the Austrians, Baden, Wurttemburg and possibly Russia and Britain to forge an anti-Prussian alliance based on the Vienna Settlement of 1815. with the proviso that should Bismarck initiate hostilities, France would be given the Rhineland in the event of a successful outcome as this was the dream of many Frenchmen, Napoleon III included. Even if Russia and Britain do not join, Austria would want to seek revenge for 1866, the south German states would see an easy exit from their predicament, and perhaps even Denmark would be willing to have another shot at Prussia for Schleswig-Holstein.
Napoleon III could also use Bismarck's own trap against him, and goad him into a war. The whole reason Bismarck was successful in isolating France was that in rewriting the Ems Telegram, not only did he manage to persuade the south German states of French aggression, but he removed any chance France could gain allies. Russia was in good stead with Prussia, Austria was militarily beaten, economically in distress and facing a resurgent Hungarian nationalism, Italy wouldn't lift a finger due to the presence of French troops in Rome, protecting the Pope, and Britain still saw France, not Prussia as a military and naval threat. France was made to appear the aggressor and there were many Europeans in 1870 who had lived through the Revolutionary and Napoleonic Wars and were all too familiar with French aggression. HOWEVER, had Napoleon III not only seen through Bismarck's ruse but even found a way to turn it against the Prussian statesman, France could gain, if not actual allies, at least sympathy. After all, Napoleon III had cultivated good relations with Britain and even joined them in the Crimean War against Russia, and in addition, gave assistance to the Italian Unification movement. Napoleon III had no clear goals beyond gaining the 'natural frontiers' of France.
It goes without saying that unless Napoleon III had modernized his military, managed to keep the south German states from joining Prussia, and gained an ally or three, the Battle of Sedan COULD still be lost. But again assuming the war happens almost like OTL-with the conditions already listed being met-France could march to Berlin. Perhaps its here that the French are defeated, but because of superiority in numbers or better military hardware, they're not driven back across the Rhine. A possible peace agreement resulting from this would award Silesia to Austria, Schleswig-Holstein to Denmark, the ancestral duchy of the Hohenzollerns could be gifted to Baden, and Framce would gain Luxembourg and the Rhineland
I say this again, however, these circumstances are both the most plausible and at the same time, most unlikely.