I don't mind the usage of "America" so much, but the term "American" just seems to be appropriated for U.S. citizens. Unfortunately, there isn't a decent term that refers to U.S. citizens, but not e.g. Mexicans or Canadians. It's possible to separate out Brazilians, Peruvians etc. by using "North Americans", but there seems to be a missing word.
“America” means “the United States of America” in English despite that not being its original meaning, nor its meaning in various other languages (Romance languages especially).
“Europe” doesn’t mean “the EU” in any language, though maybe it will shift and mean that someday.
Apparently it’s shifting as we speak, Wikipedia disambiguation page for “Europe” already lists “European Union” as one possible meaning:
Yeah in French it’s the same (at least here in CAN); if someone says “en Amérique” nobody is confused about whether they mean the continent, or asks “du Nord ou Sud?” We all just get that we’re talking about the US.