I should first commend bubb2's yeoman work in publishing the Law of the Sea treaty from 1958. If I'd read it here first it would have saved me a fair bit of time in my old International Law textbook! I'd only add that the LOST is currently under debate for revision, a revision that threatens US economic interests, but that's another matter.
I'm aware that I probably did not address your specific question as to the French sailboat in international waters confronting a US warship commanding/advising the boat to change course or exit the area. I believe I've some information that may shed some light on the matter.
First off I should say that there is very little that I've found that addresses private yachts per se. Most of international law revolves around merchant vessels of one sort or another. And it involves vessels "flagged" by their country which implies documentation, something that may not apply to all boats. I doubt that fact detracts from the overall principle of international law though regarding how the vessels are treated on the high seas.
As noted in the LOST of 1958 post, a warship, any warship, has the right to "visit and search" any vessel that meets one of the following criteria:
1) suspected of committing piracy
2) suspected of engaging in slave trading
3) is of the same nationality as the warship
4) as may be authorized by treaty between the nation of the warship and the nation of the vessel.
Posse Comitatus technically does not apply on the high seas regarding US warships and US flagged vessels. That point is somewhat obscured and finessed by either using Coast Guard vessels or CG personnel on naval vessels. Regardless, there is nothing within international law that prohibits a warship from visiting and searching a vessel of the same flag.
Now, as to the specifics of your question re: the French sailboat and US warship.
It's not piracy even if the yacht is boarded or seized. See bubb2's post for definition of piracy on that.
I find no references to any requirement that the yacht must comply with any order given by a warship of another flag. I might add that I was struck anew by how much of international law is devoted to two predominate areas; maritime law and the conduct of war. Makes sense I suppose.
As to our poor French yachtsman confronted with the arrogant forces of either US or Russian naval power I believe the below quote from Law Among Nations, 1976, von Glahn, pretty much addresses the matter and makes plain his options or lack thereof:
"Again, most individuals lack the ability to assert their rights before an international tribunal. As long as this situation prevails, it must be doubted that international law grants real rights to individuals. Only their state can take up their cause, by bringing a suit or by filing a protest or claim with another state. This means that it is the state which possesses an international legal right, not the individual."
As I read it, you may do as you please when confronted with a request or order given by a foreign warship on the high seas subject only to your good sense and, lacking that, your faith that either your navy or your government will prevail in bailing your butt out. I hope the above sheds some light on the matter.
Having said all of that, I should mention that in twenty years at sea I never had issue with a warship of any nation nor heard of any other than the Pueblo or the Mayaguez. I've had countless interogatories as to identity via either flashing light or VHF, and I know of a few "Uniform" 's anecdotally. (Interco "U", "you are standing into danger") And that included a few visits to the former Soviet Union and Israel, two country's notoriously prickly about the formalities.
In my experience, to the extent that there is any interaction between naval vessels and other vessels there is a measure of comity common to all seafarers. I stand by my original post that the OP is merely politically grandstanding without benefit of the relevant facts. He presupposes that the US Navy has either the inclination or the time to just go about ordering vessels out of their "playpen" for no good reason. I've run all three coasts of the US and never encountered anything remotely like that...but then I also made it a practice to stay out of naval exercise areas! I suspect the OP would have been singing a different tune had his acquaintance had a submarine surface underneath him! Everybody knows how arrogant those sub drivers are! (g)