A network error occurred when attempting to Sign In. Here I believe that you are trying to Sign In into Acrobat DC desktop application, is that correct? If yes, then you may try the following troubleshooting steps to see if that helps:
1- Open Acrobat>Help>Check for update and install the most recent update. 20.012.20048
2- Navigate to Acrobat>Edit>Preferences>Security (Enhanced)>disable "Protected Mode at Startup" (Win only), "Protected View" and "Enhanced Security">OK>close and reopen Acrobat
Note: these changes are only for testing purpose. Once tested, please change it back to the previous setting.