Most importantly you need to mount the drive
net use z: \\yourserver\sharename
Of course, you need to make sure that the account the batch file runs under has permission to access the share. If you are doing this by using a Scheduled Task, you can choose the account by selecting the task, then:
"When running the task, use the following user account:" That's on Windows 7, it might be slightly different on different versions of Windows.
Then run your batch script with the following changes
copy "z:\FolderName" "C:\TEST_BACKUP_FOLDER"