Although there is no longer access to the DVLA by foreign authorities, in this case, as the driver has been revealed by the Italian hire company the offence may be processed as usual with reminders and increased penalty for up to a year after which, in theory, there could be an outstanding penalty.
The op will not be on any list of outstanding offenders at ports and passports do not have addresses
He will not be in the same vehicle on future visits to France so there is no risk of a check unless he commits an offence with police involvement.
Pay up to stop worrying is the simple answer