On July 31, 2020 the French Data Regulator (CNIL) published the first information on the consequences of the invalidation of the Privacy Shield. They are the word-for-word translation of the FAQ published by the European Data Protection Board 1.
The summary is simple: “the requirements of US law […] result in limitations on the protection of personal data that are not circumscribed so as to meet requirements that are substantially equivalent to those required by EU law”. To put it plainly, “any transfer of data to the US presents a risk” 2.