Because before Sedan France was the papal protector, and after the Republic needed to maintain strong links with the Catholic Church because of anti-German/Protestant propaganda, the most suitable choose for a fleeing Pious IX is surely France and Avignon.
Spain could be the reasonable second chance, but Pious IX could accept to set in a country where in that moment he was a Savoia (Amedeo I) on the throne? Otherwise, the Pope could try to use his influence to put a Carlist on charge in the kingdom...
I see Austria-Hungary more hardly as third chance, because the Pope could have the fear to expose himself and his successors over a highly ingerence from the Hasburgs emperors...
Anyway i can see a more active Papal diplomacy which may leads towards a catholic alliance between France, Austria-Hungary and Spain againist Germany and Italy; these two countries for response decided to searching an alliance with Britain, which accepted. Russia aligned towards France and Ottoman Empire towards Germany, while USA remained neutral.
The ponder-keg of Europe in this possible TL could be only Switzerland, extremely strategical for both the alliances (it could give direct land connession between Germany and Italy, and between Austria and France); also, Switzerland is a mixture of Catholic and Protestant landers... maybe a new Swiss civil war which leads to WWI?
Spain could be the reasonable second chance, but Pious IX could accept to set in a country where in that moment he was a Savoia (Amedeo I) on the throne? Otherwise, the Pope could try to use his influence to put a Carlist on charge in the kingdom...
I see Austria-Hungary more hardly as third chance, because the Pope could have the fear to expose himself and his successors over a highly ingerence from the Hasburgs emperors...
Anyway i can see a more active Papal diplomacy which may leads towards a catholic alliance between France, Austria-Hungary and Spain againist Germany and Italy; these two countries for response decided to searching an alliance with Britain, which accepted. Russia aligned towards France and Ottoman Empire towards Germany, while USA remained neutral.
The ponder-keg of Europe in this possible TL could be only Switzerland, extremely strategical for both the alliances (it could give direct land connession between Germany and Italy, and between Austria and France); also, Switzerland is a mixture of Catholic and Protestant landers... maybe a new Swiss civil war which leads to WWI?