Hi Yannick,
Based on my experience, the issue could be caused by the wrong credentials which are being used to connect to the Office 365 Directory Synchronization interface.
1. The Office 365 Global Administrator account user name or password are bad.
2. The Office 365 Global Administrator account is a federated user account.
NOTE: The Microsoft Online Services Directory Synchronization Service cannot be used with a federated account for the Office 365 global administrator account. It must be an account that has the "onmicrosoft.com" user principal name suffix.
Can you check the following points?
1. Use a global administrator account defined in Office 365 that has the "onmicrosoft.com" UPN suffix.
2. Verify that the correct password is being used for the "onmicrosoft.com" global administrator account by attempting to logon as that account at: https://portal.microsoftonline.com
3. Run through the Directory Synchronization Configuration Wizard supplying the user account with "onmicrosoft.com" UPN suffix and an enterprise admin account.
If the issue persists, please let me know the current version of Dirsync. You can navigate to C:\Program Files\Windows Azure Active Directory Sync, and right click configwizard.exe(choose properties). You can see the file version in Details tab. Also, do you install the Dirsync on DC or else?
Regards,
Johnny Zhang