I know that fatturaPa accept certificate from the trust list here Trusted List listed on this page https://www.agid.gov.it/en/platforms/qualified-electronic-signature/qualified-certification-service-providers. That is the list of trust service provider of Italy.
You can find all trust list (including italy and france) here:
As it seems that all trust list in Europe are made to be compatible and aim at cross border use.
Do you know if we can sign digitally invoices and notifications we send to SDI with a certificate from a CA which is in the Trust list of France ?