Revalidation
The examiner makes the entries and signs the licence revalidation page so you do not need to take it to the authority.
You must also fill in the appropiate revalidation form. With regard to the UK administered licence, the examiner also completes and signs a certificate within the the UK revalidation form SRG1119 but that is then sent to the the UK CAA. The form simply informs the authority that you have revalidated, with the details.
If your licence is administered in Italy then you must use the appropiate italian form and send it to Italy or if administered in France to the french.
The forms used by each country are unlikely to be similar and therefore may not be accepted.