Quite. French Empire may have its issues as a name, and is not the most precise name, but all the things it can refer to all harken back to a specific time period of French history, the nineteenth century, which comes after a very notorious and very large complete reformation of the French state (the Revolution of 1789). You couldn't name an Exploration French civ "French Empire", and you couldn't name a Modern French Civ "Ancien Régime France" or "Capetian France" or whatever other names an Exploration France could use.
In game terms, we have a clear Exploration Civ (Ancien Régime/Capetian France), a crisis period (the Revolution) and a new civilization (the French Empire) emerging. This works.
Likewise England, which cease to exist as a sovereign country around the end of the Exploration Era, to be replaced by the United Kingdom of Great Britain (later: and Ireland, still later: and North Ireland), a separate polity born out of the union of England and Scotland (and the gunpoint addition of Ireland to the wedding). The crisis is harder to pinpoint, though you could make a case that the English Civil War and subsequent Glorious Revolution are probably it.
In opposition, America and United States are just two perfectly interchangeable names that can both equally apply to the entire 1789-2025 period in the United States of America (of which they're both shorthand forms). The political structure and constitution of the polity remain largely the same through much of the period, and it does not go through a significant transition from one nation to another (eg, England - Great Britain). So having both names describing different things is infinitely more awkward, especially when the "Modern" america is clearly. There are multiple crisis candidate, but they don't lead to a fundamental change in the nature of the country.
On the other hand, *other* Atomic nations would also be bad. the French Empire and *modern* France are substantially the same nation (just without a colonial empire), likewise Great Britain and the United Kingdom, etc.
Which is the core difficulty here. If two civs in two different periods could exchange name and both names would still feel entirely appropriate (eg, call a Modern USA "United States" and an Atomic one "America"), then they aren't separate civs at all.
Nazca is not a bad option.
