When it comes to a classic fileshare with a need of ACL, there is no Azure solution yet, but also in this case, you can use Azure to keep those fileshares available.
Sometimes there are use cases where you need to have caches for file servers and storage within a branch office. In the past, I needed expensive storage devices or complex software, or I used a Distributed File System replication to transfer files. With Windows Server 2016, we got storage replication, which gave us new opportunities to think about. You can use this kind of replication to move files or back up data into the cloud.