I think you can simply Download all the file from your file manager in Zip format. And simply Extract them in your Local Host .httpaccess folder.
The difference is you have “Public.html in the file manager of your web server and here in local server, you have the httaccess folder.
Make sure that you have created the same database name as your web server database. It should work then.
Another way is,
Simply install a WordPress site in your Local server. Then replace the downloaded file. Note that you have to extract your zip file and then replace (copy paste) the file in your local server WordPress/WP folder (of your httaccess).
Firstly Replace the plugins. then replace the other folders one by one.
Hope this will help the issues.
Goodluck