You can fulfill this requirement by using the following steps - 

1- Open Mass File Download App --> Go to the About Mass file Download Tab.

2- Scroll down and click the File Download Configuration section which is under MFD Page Configuration Settings and enable below two toggles - 

         I) Download Files in ZIP format

        II) Download the Zip of Files in SubFolders

3- Click on the Save Button.

4- Now Go to the Mass File Download tab and Download Files & Attachments.

5- Open Downloaded Zip File, Here you'll see the Folders named as the Record Name.

6- Under this record name folder, it's showing all Files and Attachments which are belonging to the specific records.