Azure Files itself doesn't have a built-in feature to archive files to Blob storage automatically
However, you can use Azure Blob storage lifecycle management policies
https://video2.skills-academy.com/en-us/azure/storage/blobs/lifecycle-management-overview
To achieve this you can some workflow like this
start with azure function (you can run daily) to list files in Azure Files and check their last modified date and transfer those files to Blob Storage
then you can configure a lifecycle management policy to move archived files to a cooler storage tier