Hi Christophe,
I understand that you want to migrate your site collection from on premise environment to Office365. I have done a research and found an article: Prepare to migrate to SharePoint Online.
Since the issue is related to SharePoint on premise environment and we may need to do some customization during migration. I suggest you post your question to our SharePoint forum for more professional help. Because our forum provides limited support for on premise environment. We appreciate your understanding.
Thanks,
Kevin Hu