No, what I am saying is, the word is not Ancient Greek and Modern French alone: the word is Modern English, too, and found in many other modern tongues touched by Greek. It just isn't used anymore by Americans -- at least not since the 1960s onward. Sort of like the words "flippant" or "paragon," the words "licentious" or "debonair." If I asked most people what those words meant, I don't think they could answer. They might say, "I used to know at one time when I was a schoolchild," but I don't think many American adults would be able to define those words. Common words. English words. Like acme.
If you look on Wikipedia, you'll see something even I didn't know: apparently in the 1950s, the term "acme" was used as a catch-all to refer to American corporate enterprises, as they were the "acme" (or pinnacle) of entrepreneurship. So in other words, anyone alive today who was at least somewhat in touch with current affairs back in the 1950s would know what the word "acme" means. Pretty cool.
Besides, $20 says you're basing the French argument on WWWJDIC, the very same place I looked up アクメ months ago. (See attached picture for more details.) For the record, I don't dispute it but I also don't blindly accept it just 'cause JDIC says so either. The study of gairaigo can be very intricate, even insolvable, because of how much confluence there was from Portuguese, French, German, and American (English-speaking) sailors all in the same period of 100-150 years. The languages are so very, very similar in many ways and share so many common words that it can be difficult to say with certainty who gave Japan what. Words like pan we can guess were Portuguese simply because we have written Japanese records using the word prior to the arrival of the first non-Portuguese non-Dutch sailors. But words like coiffure can prove more difficult: was it the 19th-century French or the 20th-century Americans who introduced that term to Japan? And what about resume? Or recipe? A lot of words which are entrenched in English and French are hard to separate out etymologically when it comes to Japanese gairaigo.
I guess that's all I was trying to say.