Another possibility is that Nice and Savoy are given in the treaties of post Napoleonic Europe to the House of Piedmont Sardinia.
They already were. To be fair, the territories were Savoyard prior to the French Revolution, and then the French occupied both Savoy and Nice in the 1790s. IIRC, the initial Treaty of Paris in 1814 that ended the Napoleonic Wars was pretty lenient on France—France kept her 1792 borders: Saarbrücken, Saarlouis, Landau, Montbéliard, the part of Savoy with Annecy along with Avignon and Comtat-Venaissin. There was no occupation of France, and no indemnity either.
After Elba and Waterloo, the second Treaty of Paris was harsher: return to 1790s borders (except they kept Avignon & Comtat and Montbéliard), loss of Saarlouis and Landau, some communes near Geneva, and of course Savoy. They also had to pay a 700 million franc indemnity—daily payments were something like 380,000 francs or £16,000—and they had to host (and cover the expenses) for a 150,000 men occupational army of coalition troops. Like post-war Germany, France was carved up into various occupation zones.
But that actually happened.
Exactly.
I meant Nice and Savoy are become House of Piedmont ruled lands permanently.
That's sort of what the post-war treaties did. The reaction against Napoleon and the Revolution attempted to turn back the clock where applicable—the prevailing idea of legitimacy is whatever that country held was restored to it. The main issue is that if that country decides to depose of those lands later on down the line, nothing is stopping them. Many in those provinces believed that the House of Savoy favored Italian speakers for government jobs over French speakers. In 1859, some thirty citizens in Chambéry called to be annexed to France, but it wasn't a popular idea overall: there was opposition in northern Savoy. Alternate suggestions floated the idea of Savoy joining Switzerland instead, favored by Great Britain.
Pretty much as soon as the Treaty of Turin was signed, the deal was done. It was agreed plebiscites should be held in both provinces, since both provinces had to "agree" even though the outcome was already determined. To deal with resistance in northern Savoy, the plebiscite was coupled with the option to create a duty free zone. Given that the treaty was signed and the territories handed over
before the plebiscites, there's certainly some doubt about how free and fair they were. The 1850s was the height of the "authoritarian" empire in France, after all...
I suppose one way to prevent it is greater resistance to the idea. I think so long as the provinces are handed over first, the plebiscites will be in France's favor: both Sardinia and France had reason to want their success, since the two territories were Napoleon III's desire to aid Sardinia against Austria. Another idea might be greater British resistance to the idea... it might provide the smoke needed for the Swiss option to be more attractive for northern Savoy. It's not Sardinia keeping it, though...