Thanks to Rafael for the tests and answers that allowed me to understand the problem. Namely: I tested with a already registered user.
The re-registration of an old subscriber results in the reactivation of his subscription but the personal information (last name, first name and other custom fields) are not updated: this can only be done from the “modify subscription” link present in the newsletter… pity ! ??
Other subject : Having added custom fields to the subscription form, i noticed that their order wasn’t the same in the custom profile page as in the subscription page… unfortunately there’s no way to modify it.
Thanks again to Rafael and MailPoet support !