Who cares, anyhow?
Monte Carlo is in the country of Monaco, so what?
Monaco is less than a square mile, the whole country is so urbanly congested, it makes Monaco and Monte Carlo almost synonymous.
The country is surrounded on three sides by France, and the fourth side by the French Riveria. There are no border checks, and if you make a wrong turn, you may find yourself in a tunnel that comes out in Nice.
If you were there and thought you were in France, what would be the biggie? Heck, pretend it's in Italy. That's only ten miles away still with no border checks and everyone there is using the euro!