You don't have to believe it. It's the working of the Ukrainian tax code that says that when you become a private entrepreneur in Ukraine you become tax resident there. You can google "FOP Ukraine" and see for yourself.I really find it hard to believe that this should work.
Of course you can't live in France and pretend to pay taxes only in Ukraine because you are tax resident there.
Who cares about registering a company in Ukraine when you can register a US LLC/ UK LLP and make that the front of your business? You then invoice the offshore company for your services and pay 5% taxes accordingly in Ukraine.you can't have company, only PE option which limit options a lot.
The biggest part of profits are left untaxed in your offshore company.
Oh yes, this is a CFC!
You have to declare all of the CFC income in Ukraine but "if the total aggregated income does not exceed EUR 2 million you are exempted" and since you are not spending any day in Ukraine the place of effective management of LLC/LLP is not Ukraine.
The only thing that has to be seen is how Ukraine treats transparent entities.
If those are seen as transparent you will have to add a capital company in the mix.
If those are seen as opaque you should be good.
Of course all of this has to be verified with a ukrainian legal person but if you are willing to be costanly on the move and never stay enough in one place to trigger tax residency in that place i don't see why this should't be working.