So, how can we allow for the Franco-Prussian War to either:
-Not be a completely crushing Prussian victory
-Be a French victory
-Not happen
Bonus points if Germany still unifies and/or Napoleon III keeps his throne.
1. Fairly easy to do, in a number of ways. Here's just a few examples;
* The French never (accidentally) occupy Wörth, and so the subsequent battle never happens, or rather happens on French terms, who, prior to taking Wörth, held the best defensive location for miles around.
** Even with Wörth, the French could have won the battle if the Prussian commanders hadn't been able to re-establish control over their units, who had started to march wildly in random directions during the first few days of battle in confusion. Alternatively, if the French had taken the opportunity to attack during these first few critical days, they could have broken the Prussian lines and forced a Prussian rout from the field altogether.
* The French are more aggressive at Borny-Colombey, meaning that their main army is never trapped in Metz.
* The Siege of Strasbourg continues, with Uhrich not surrendering to the German forces, meaning the Germans have to either encircle the city, leaving forces behind to prevent a breakout, or take the time to capture it street-by-street.
* After smashing the Prussian First Army and forcing the Second to stall its advance at Gravelotte, the French forces either attack, or remain held up in their defensive positions, instead of retreating to Metz as IOTL. Thus Bazaine's
Armée du Rhin is never trapped in Metz and forced to surrender, and thus Mac-Mahon's
Armée de Châlons isn't caught strung out near Sedan and defeated in total.
* Even assuming the above battles goes as per OTL, if, at Sedan, Mac-Mahon initially appointed Wimpffen to command, instead of Ducourt, the French could have broken out of the city and continued to fight on.
Really the biggest thing to keep in mind is that, even after Sedan, the French continued to fight on. For example, the French won a decisive victory at Coulmiers some two months after Sedan. Even assuming an OTL war until the above, if d'Aurelle's Armée de la Loire hadn't stopped its march towards Paris, his forces and Mac-Mahon's might have linked up outside of the capitol, and thus been able to keep the Prussians out of the imperial city. Considering the events of the OTL Paris Commune, its quite certain that the French citizenry would have risen up against the invading German forces (as they did at Metz, for example), and soon the German forces would have been forced to try to fight a war deep in enemy territory with their supply lines under continual harassment by partisan forces.
2. Harder to do than the above, but still doable. The best bet for the French would be to sit on the defensive along the Rhine, as Frossard called for, repeal the German attacks with their superior rifles, and then advance into the southern German states and 'liberate' them, hoping to bring Austria into the war at that point.
3. Fairly easy really. Between 1866 and 1870, right up into the last months and weeks before the war, there were plenty of opportunities for PODs which would have led to a different diplomatic situation and prevented the war from happening at all.