The way I see it, the quote means the United States of America can't be in the Americas at all.
And it has to be Voltaire who says it.
Here's one possibility.
Amerigo Vespucci's family becomes a lot more wealthy and influential, their name is as well-known as names like Columbus and Shakespeare.
The continents of the New World are still named N. and S. America.
OTL, the Dutch colonized South Africa in the 17th-18th centuries; they find plenty of gold and diamonds.
The colonies become autonomous. Amerigo Vespucci was apparently Italian, but his descendants can be all over Europe, and some of them are in South Africa, and for whatever philosophical reason the colonists are badgered into naming their new nation, America.
The colonies are really a loose confederation of autonomous states, similar to a precursor to OTL's UN, but they want to present a united front to everybody else, so they call themselves the "United States of America."
Or, these can be British colonies in South Africa, or India.
India wasn't really a single, unified region like it is today, it was a collection of small kingdoms, and rather than name the region after one of those kingdoms, it gets named after Amerigo Vespucci because one of his descendants was a big shot in British colonial India in the mid-18th century.
So it's really a loose confederation or something.
I know I've left out lots of detail, just in case these aren't such good ideas.
Is any of this plausible?