The following information has been provided by the London offices of the French Ministry of the Economy and Finances in relation to paperwork now required by drivers entering France:-
Controls have been restored at French borders that mean foreigners will be refused entry with certain exceptions, including for workers carrying goods. There are no restrictions on the circulation of trucks, however, drivers must carry the French version of two signed waiver certificates or they will be refused entry.
You can download the required waiver certificates (and unofficial courtesy translations in English) to allow the movement of trucks in France. Drivers must carry these at all time and they must be completed by both the driver and their employer
Download here
1. French personal travel waiver certificate (attestation de déplacement dérogatoire) which must be completed and signed by the driver.
2. French professional travel waiver certificate (justificatif de déplacement professionnel) which must be completed and signed by the employer (i.e. the driver’s manager)