This answer is limited to the U.S., where I have taught and practiced in this area, since I don't know much about French law in this area.
The bottom line, is that there aren't really full fledged tax havens in then U.S., although some U.S. states provide a fair amount of protection from creditors of the person forming a trust there. Asset protection and tax reduction are two distinct goals of "havens" and U.S. jurisdictions only do much for the former, not the latter.
A numbers of states, such as South Dakota, Wyoming, Nevada, Delaware, and Alaska have relaxed traditional rules that disfavor "dynasty trusts" designed to allow trusts to endure with "dead hand" control for many generations.
These states also impose only modest state taxes on trust and shell company assets (Delaware charges rather high flat fees for setting up entities there but not a tax based upon the amount of assets the entity formed there holds, or its profits.)
And, perhaps most importantly, these states have put in place strong protections for trust assets from creditors' claims and allow high levels of privacy for firms and trusts established there. Federal law anti-money laundering laws, some of which were due to take effect on January 1, 2022 but have been delayed due to delays in adopting implementing regulations, also require significant disclosures of entity ownership, undermining this historic benefit of these U.S. jurisdictions.
But none of that shields assets in these states from federal income taxation, which while hardly the highest among developed countries (U.S. corporate tax rates, in particular, were cut dramatically starting in the 2018 tax year), is also nowhere near the low rates of traditional "tax havens" like the Cayman Island and Nevis (these island nations typically finance their governmental operations primarily with customs duties and user fees).
This is why many big U.S. multinational technology companies try to locate much of their intangible "hot asset" profits from their intellectual property rights and financial investments in jurisdictions like Ireland, instead of the U.S.
It is possible in many cases for businesses based in Puerto Rico to be free of federal income taxation, but only in exchange for paying significant Commonwealth of Puerto Rico taxes. And Puerto Rico has not adopted laws that make itself attractive as a creditor-protection haven.
So, while some U.S. states are taxed at favorable rates relative to other U.S. jurisdictions and provide some asset protection, it isn't at the extreme levels associated with foreign asset protection and tax havens like Luxembourg, Switzerland, the Cayman Islands, and Nevis.
The efficacy of these protections is also overstated.
For example, I am familiar with a case where someone attempted to use South Dakota entities and trusts to shield significant assets from an IRS tax creditor and this effort failed dismally.
The option of an involuntary bankruptcy case or federal securities fraud claims can also often pierce domestic asset protection trusts and entities. And, U.S. judges are not reluctant to incarcerate debtors with associated asset protection trusts that U.S. judges believe that the debtors have a de facto ability to access for many years, in rare cases in excess of a decade.
On the other hand, while these jurisdictions in the U.S. offer only half-measures of protection, they do provide people relying on them with low levels of corruption in administering their hidden assets, and an ability to enforce their own rights in a relatively predictable and reliable legal system.
Another point worth keeping in mind is that many famous tax havens invest their assets in the U.S. securities market as non-resident foreign corporations controlled by foreign persons and not affiliated with U.S. persons.
For example, a Cayman Islands trust with a Cayman Island's trustee and Columbian beneficiaries can invest in companies traded on the New York Stock exchange without being subject to U.S. taxes on the dividends and capital gains that the Cayman Islands trust earns on those investments.
This is something that a company or trust organized under the law of a U.S. state cannot do, because U.S. entities are subject to U.S. income tax on their worldwide income. A parallel U.S. federal income tax regime also imposes high U.S. taxes on "Controlled Foreign Corporations" that are beneficially owned by U.S. persons even though they are organized abroad.