U.S. tax law is the first and biggest barrier. It is unlikely that U.S. expats in France would face U.S. taxation in practice, and when it is owed, the tax burden is likely to be very modest.
Earned income of expats up to a substantial threshold is exempt from U.S. income taxation ($104,100 USD in 2018), and the foreign tax credit reduces any U.S. tax that is due by any tax paid abroad to a foreign government.
In general, the higher income and passive income taxpayers who are potentially subject to U.S. taxation, since their income isn't entirely excluded from U.S. income taxation, pay higher tax rates in France than they do in the U.S. So, no net U.S. tax is due. The tax rate on a typical high income earner in France is 58.1%, which is typically more than enough to eliminate U.S. federal income taxation (with a top tax bracket of 37% in 2018) through the foreign tax credit (and of course, expats are not subject to U.S. state and local taxation because they don't reside in any U.S. state or locality).
(The estimate above isn't quite right because it doesn't break the total down by types of tax, French social insurance and wealth taxes aren't eligible for U.S. foreign tax credit treatment, but French income tax rates still exceed the top U.S. income tax bracket at 71,899 Euros as of 2017 at which point the marginal income tax rate is 40% and the top French income tax bracket is 45%, both of which still exceed the top U.S. income tax rate; someone with less than 71,899 Euros of earned income would have that income excluded from taxation under U.S. law. Also, at lower incomes where French income tax rates are lower, U.S. income tax rates are also lower.)
The U.S. estate tax burden could be a form of double taxation at the death of an expat, but that only impacts U.S. citizens with more than $11,180,000 USD individually or married couples with more than $22,360,000 USD. No doubt there are a few dual French-US citizens who have to worry about that, but not many. And, there would be at least partial offsets for taxes due at death in France, even then.
Tax Haven Income
The sort of scenario where a French-US citizen would be most likely to face U.S. taxation would be one where the French-US citizen has unearned income from financial accounts in the Cayman Islands or some other tax haven that is not subject to French taxation based upon territoriality (i.e., subject to exception discussed below, France does not tax income earned abroad by French citizens) but is subject to U.S. taxation due to its citizenship based taxation. The U.S. income taxes due on this income would not benefit from any foreign tax credit because no taxes are paid in the Cayman Islands or similar tax haven on this income.
However, while France purports to have a territorial tax system, it actually taxes the global interest and dividend income of its citizens just as the United States does, so only unearned income that is not of that character would be subject to U.S. taxes but not French taxes, further narrowing the gap and the number of people paying extra U.S. taxes.
This is not a very sympathetic bunch of oppressed French-US dual nationals. It is also a group of dual nationals whom the U.S. does not need the cooperation of the French government to impose taxes upon, since the information relevant to the income would not be controlled by the French government, or even available to the French government.
Also, the dual French-U.S. citizens intending to benefit from these tax havens could probably fairly easily arrange to indefinitely defer taxation of this income by setting up some Cayman Islands companies to hold these assets without too much of an undue burden. The holding companies might need to invest, in part, in operating businesses in the Cayman Islands rather than merely passive investments to circumvent some of the more direct "foreign personal holding company" tax rules in the U.S. But, the tax law passed in 2017 that took effect mostly in 2018 makes it easier than it used to be to defer taxation of or eliminate taxation of foreign income.