Old hotmail account is locked, and the recovery mail box has been deleted

Hello,
I am writing this question from my professionnal mail because I don't have any other microsoft account.
I plugged my old Xbox360 yesterday, and I can not access my profile for the reasons specified in the question title. I know the password of my account , but in order for me to unlock the hotmail.fr box, I have to get a code from another mail box that has been permanently deleted due to inactivity, therefore I am unable to verify my own account.

Is it possible to bind another mail box to this hotmail.fr account ? And if not are there ways to unlock my situation ?

Thanks.

Quick edit : As told in the ticket, the hotmail.fr account is really old (maybe 10 years old'ish), so all my attemps to verify the account with the option "can't access any mailbox" were rejected automatically since I don't remember all the details like old credit card infos (excepted the name). I do have the console, the profile name and the console ID but it wasn't enough apparently.

:)