Exactly my point. France did prop up Sardinia-Piemont though, helped them in the War against Austria, for example. In teh end, France enabled Saridnia-Piemont to unify Italy, but that didnt make Italy a loyal ally, as Napoleon III had hoped. Instead, as you said, it even kind abackfired as there suddenly was one more (relatively) powerful neighbour.
So, Napoleon III. surely wasnt all that grand in international strategy... but at least he did have a clear-define dobjective (THE base condition for a good strategy) in the German War.
So... but, before we lose focus again, lets stay on topic:
Wilhelm lets the war drag on. Prussia makes gains in Bohemia, but eventually France intervenes. Prussia cannot win against both, even with Italian help (and I dont think therell be a French-Italian theatre, for that matter).
So, in the end, I could imagine a peace solution like that: France wins the West Rhinish Territories, including Palatinate (but excluding Rhine Hessia, there is just nothing to compensate Hesse-Darmstadt with). Bavaria is compensated with the East Rhineland and Westphalia (thus Prussia loses all western possessions). Austria Wins (back) Silesia and Lombardy. Hannover wins Brunswick and Southern Oldenburg. Saxony may win back parts of all of what it lost 1815. Nassau wins the Prussian Wetzler exclave, and the Hesses the Prussian territories in Thuringia.
So, what happens now, in that situation?
Alternatively, there might be a chance Russia intervenes, and that would change everything... but that chance is very small. But if it happens, I would say the Prussian side wins, in which case we the IOTL consequences, plus additional losses for Austria and France: France might lose the Alsace, or even also Lorraine (the Province, not the small part Germany took IOTL), Austria might lose Bohemia (to Prussia), Galicia (to Russia), Dalmatia and Tyrol (to Italy)...
What happens in THAT situation?