I doubt that France could intervene successfully. The problems which appeared during the mobilization and the concentration of the French Army in july 1870 would also happen in 1866, and the French would even be in a worst shape than in 1870 as the reforms of Niel haven't even been launched. By the time, the French would put a foot into Rhineland, Hanover would have been for long defeated and occupied by the Prussians.
What's more, the mobilization that Napoleon III was about to order IOTL was to bring Prussia to peace negociations, not to commit France into a war.
Unless you prevent the defeat of Sadowa, all you can do is making the treaty of Prague less harsh for Austria.
Since Luxembourg was the price of the French neutrality, I imagine that by mobilizing, Napoleon III could forget it.
Preventing a united Germany to appear at the border would continue to be the main priority of both French and Austrian foreign policies, what makes an alliance necessary.
Past Napoleon III, French colonial expansion would lead to clash with the UK (Egypt, Indochina...) and would exacerbate French anglophobia (remember the Fashoda crisis). With the Great Game underway in Central Asia, it seems logical that France would support Russia against the UK. In turn, this would lead the Ottomans to seek protection of the British against Russian expansionism in Caucasus and Balkans.
Although Italy should continue to be aligned with France (the Italians asked for the approval of Napoleon III before accepting an alliance with Prussia in 1866), if the problem of Rome isn't quickly solved, this could push Italy in an alliance with the British.
What's more, the mobilization that Napoleon III was about to order IOTL was to bring Prussia to peace negociations, not to commit France into a war.
Unless you prevent the defeat of Sadowa, all you can do is making the treaty of Prague less harsh for Austria.
Since Luxembourg was the price of the French neutrality, I imagine that by mobilizing, Napoleon III could forget it.
Preventing a united Germany to appear at the border would continue to be the main priority of both French and Austrian foreign policies, what makes an alliance necessary.
Past Napoleon III, French colonial expansion would lead to clash with the UK (Egypt, Indochina...) and would exacerbate French anglophobia (remember the Fashoda crisis). With the Great Game underway in Central Asia, it seems logical that France would support Russia against the UK. In turn, this would lead the Ottomans to seek protection of the British against Russian expansionism in Caucasus and Balkans.
Although Italy should continue to be aligned with France (the Italians asked for the approval of Napoleon III before accepting an alliance with Prussia in 1866), if the problem of Rome isn't quickly solved, this could push Italy in an alliance with the British.