As I know, you can copy the data stored in the VM disk to the on-premise disk. In Windows, you can use the tool directly. For example, you can install the FTP in your VM and then connect the FTP with the FTP tool, and finally, copy the files from the VM to your on-premise machine. And in Linux, you can use the SCP command. But all these ways are complex. You need to copy files or folders one by one.
I will suggest you mount the Azure File Share. Mount the File share both on your VM and your on-premise machine. Then you can share the files between VM and on-premise machine if you copy the files you need into the mount point. Also can share with other machines if necessary.
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