For example, the people who live there, les Americains, most commonly refer to their country as "the U.S." in casual contexts. (At least in my experience as an American.) "USA" is generally used when someone's emphasizing patriotism in their statement, "United States" is more formal, and "United States of America" is barely said except in songs and celebratory announcements. Lastly, "America" is also quite common, though less so than "the U.S.," and again slightly emphasizes patriotism.
I know it's les États-Unis or les E.U. in French, but which is most common, and are there others?