As a fraud. The United States and Great Britain, at least, both reported opposition to it. Great Britain filed a formal protest. An American reporter called it the greatest immoral fraud of a vote ever perpetrated. The British Foreign Secretary famously said, "we are neither entertained nor edified." He also called the process a farce publicly.

There were similar sentiments in other places, and a decade later the Germans reminded the French of their annexation of Savoy when annexing Alsace and Lorraine. This led to the rather Orwellian measure of changing the history books to talk of the Incorporation of Savoy. Some bitterness over this lasted at least until the Second World War and probably after. Notably Savoy sued the French government when it tried to change the laws agreed to in its treaty of annexation the 1920s. The International Courts ruled against France but this had little actual effect.

So yes, contemporary opinions largely match your skepticism.

I've never heard of this 1848 annexation attempt. Could someone please expand on it?

Napoleon III restricted his ambitions to Savoy and Nice, that was maybe what preserved the peace.

The King of Belgium was worried but I don't know if he condemned.

Switzerland protested and sent letters to the Congress of Vienna signatories. They were worried about the french expansion and a possible encirclement. Plus they were benefiting from a "neutralized zone" in North Savoy that a French annexation could question.

About the Four Great Powers of Congress of Vienna : Russia and Austria disapproved but didn't go further. But it must be said that Russia ( in Crimea ) and Austria ( in Italy ) have just lost a war against France in 1860. Prussia too, maybe in return for the french neutrality in the coming Austro Prussian war ?

Great Britain's reaction is interesting. They disapproved obviously notably after the Swiss protest, but even if they enrolled 130,000 volunteers "just in case" they had plenty of reasons to not go further aswell. First of all, they didn't want to go to war. As Queen Victoria said in letters to the King of Belgians in January 1860 :

This country never would consent to be entangled in a war for this Italian quarrel. . . .

and

The feeling of all parties and this whole country is to let Italy settle its own affairs and England to keep quite out of it. . . .

Plus, Franco-British ties were already important, with the Crimea, the cooperation in Middle East and China affairs and in particular the Cobden–Chevalier Treaty signed in January 1860. Peace is business and as Lord John Russell said :

"The powers of Europe, if they wish to maintain peace, must respect each other's limits, and, above all, restore and not disturb that commercial confidence which is the result of peace, which tends to peace, and which ultimately forms the happiness of nations."

Queen Victoria and the House of the Lords knew that this free trade agreement was a bargaining chip and that they were dupe but why die for Chambéry ?

Besides, GB was financially supporting Victor Emmanuel II, Cavour, Garibaldi, and their project of Unità, notably against the Two Sicilies, for business again could have prevent a return on investment.