The conversion of French-derived ending “-re” to “-er” was a reform in American spelling, done by Noah Webster. The reason Americans use “plow” instead of “plough”, among other reforms, are due to him.
“Meter” is the correct United States English spelling, as is “center” and “color”. I am unaware of there being a generally accepted international standard for the English language.
I would be very surprised if there was a “correct, official, internationally-approved spelling” of any unit. Spelling is language-dependent. The unit is not. The German spelling, as someone said, was chosen to match the sound of the original, not the spelling. And the Chinese uses a semantic meaning instead of trying to match sound or spelling: gong1chi3. “gong1” means “public” or “standard”, and “chi3” is a traditional Chinese unit of length. A meter, in Chinese, is simply “the standard unit of length”.
To even have the concept of spelling, you need an alphabet (well, you might be able to get away with a syllabary). There cannot be any such thing as an “correct, official, internationally-approved spelling” if there is no “correct, offical, internationally-approved” alphabet, and to my knowledge, there is none.
One could argue that the (French) creators of the word spelled it “metre”, and therefore the correct English spelling is “metre”. That’s a silly argument; if you buy that, then you’d have to spell “taikun” instead of “tycoon”, “jagganath” instead of “juggernaut”, and “al-khuwarizmi” instead of “algorithm”. English is a language that has historical precedent for spelling changes.
The BIPM doesn’t have any jurisdiction over U.S.A. English spelling of “meter” any more than they have jurisdiction over what the Chinese name for “meter” is, or over what Cyrillic letters the Russian Federation uses for the unit. They get to define the unit itself, which is, IMHO, more important anyway. It just so happens that the BIPM uses the U.K. English spelling in official reports – well, they had to choose SOME language. If they chose Korean, would you insist that all of us would have to write the Hangui for “meter” as the “correct, internationally-approved spelling”?
It isn’t. A meter is 1250/381 feet. Putting all those digits in a decimal representation is just showing a misleading amount of complication.
I hope not. Change “year” to “second”, and it’d be good.