I just got news about this issue.
Microsoft Support called me back and told me I had another global administrator on he account. I forgot I had invited another member of the team a few weeks ago but that person hadn't yet accepted the invitation. The invitation was still working, which was good news.
So the invitation was accepted and that team member was able to enter my account details on the Azure portal and revoke my MFA configuration.
After that, I was able to login again :D
Anyway, I asked the Support technician what would happen if there is no other global administrator. He told me that I had to provide a proof of my identity and this validation process might take more than 24 hours.