Hi @Raphael
Have you tried by any chance with Azure Content Delivery Network (CDN) or by configuring the storage account with read-access geo-zone-redundant storage (RA-GZRS)?
Reference:
https://azure.microsoft.com/en-us/products/cdn/
https://learn.microsoft.com/en-us/azure/cdn/cdn-create-a-storage-account-with-cdn
https://learn.microsoft.com/en-us/azure/storage/common/storage-redundancy#read-access-to-data-in-the-secondary-region
If you plan to test any of these, I'd be glad to hear how it suits your needs or if you discovered any limitations in your specific scenario.