Joshua – thanks for replying to my question and confirming what needs to remain confidential. If there’s nothing specific you can think of other than admin user data that needs to remain confidential, then I would be confident in saying that’s all you need to worry about (unless you have any plugins which have usernames/passwords, or similar set in their settings).
What I would recommend to achieve this is to create a new admin user for the user at the franchise from within your WordPress admin, then do a full database export from your hosting control panels/cPanel’s phpMyAdmin.
Once you have the SQL file downloaded, simply edit the file in a text editor and remove the lines from the wp_users table that correspond to your own admin users, leaving the new franchise admin user in place.
Once this is done, delete the franchise user from your WordPress admin area and then send them the modified SQL export file.
The only other sensitive thing would be your sites wp-config.php file as this will contain your database connection details (server, username, password).