Should you need, I also speak French. We can switch this conversation to the French section of the forum
So you said that users can log in backup_copy but not in backup_copy/backup. So just have your users log in the backup_copy directory and in there, put a sub-directory per data type (you said you wish a per-data backup model) with proper ownership and permissions :
backup_copy/data_group1
backup_copy/data_group2
...
Set ownership to each data_groupX folder to Root and backup group BackGroup1 ; BackGroup2 ; BackGroupX as required.
Assign each user to the groups he should be able to backup to : User1 is member of BackGroups 1 and 3, ...
Set permission to 770, so the Root can do it all, so can the appropriate group, but other groups can not do anyting.
Have your users putting their data in the appropriate folder.
This way, all users can log in (you said you achieved that part already)
Once in, they can add stuff only to the proper sub-folder
But honestly, to do per data backup managed on a per user basis does not make much sense... Either you really manage your data at data level and do it with infrastructure components, or if you do it at user level, then you do user-level backups. But trying to do a per-data backup with a per-user approach is not the best way.