For nothing less than a matter of colour, the Third Republic was established.
Following the abdication of Napoleon III and the proclaimation of the Republic in Paris, Bismarck had demanded the tenure of elections before engaging any peace talks. Whilst the Republicans campaigned on a bellicist program, the Monarchists (divided between Legitimists, reactionnary partisans of the Bourbons, and Orleanists, more liberal partisans of the Orléans) easily won on peace promises. Adolphe Thiers, who had been a figurehead of the July Monarchy, was appointed head of the Provisional Government: as such, he managed to smash the Paris Commune, pay war reparations to the Germans and to bring balance to a troubled France.
All monarchist hopes relied on one man: Henri, count of Chambord, known by the Legitimists as Henri V. The posthumous son of the Duke of Berry (himself son of Charles X), better known as the "Miracle Child", he had lived for most of his life in exile, and without descent, he would have been succeeded by his cousin and Orleanist pretender, Philippe d'Orléans. The ceremony, the throne, the coach, everything had been planned. Except for Henri V's personal ideas of France: at every attempt, and despite the less radical monarchists' efforts to persuade not to do so, the would-be King of France insisted that the White Flag of his ancestors must be restablished, to replace the Tricoulour Flag. Even for the most rabid monarchists, such an idea was unthinkable. Disappointed by the Bourbon's claims, and the impossibility of a quick Restoration, most of the Orleanists, including Thiers, approached the Republicans. In order to counter this upheaval, the Assembly replaced by 1873 Thiers by Marshal de Mac-Mahon, a Legitimist, as President of the (provisional) Republic. But again Chambord refused. The monarchists agreed to draft provisional Constitution and Republic, waiting for the inflexible Chambord's death, and further preparing the next Restoration with the Moral Order policy implemented by President of Council Albert de Broglie. Unfortunately for them, the strengthened and united Republicans used the new law legislations to slowly conquer power, leading to the establishment of the Third Republic.
Henri de Chambord died in exile in 1883, will all hopes of a Third Restoration vanished. Was he really so stubborn or reactionnary? Or did he express such demands to be never forced to reign?
What if Chambord had accepted the Tricoulour Flag and was established as King of France?
With the Third Republic nipped in the bud, France, and the world would have taken a different turn. In France itself, even with the more liberal Orleanists, it's the anticlericalism and educational program that characterized the Third Republic that disappear, or at least become quite doubtful. And for France's foreign policy? Do the French monarchy would have led to an earlier war with Germany, a slowed down colonization, more difficult relations with United Kingdom but better ones with conservative monarchies such as Russia?
I would like to see your personal opinions about this upheaval, and then I will try to make a little timeline.