You have to connect to the FTP, then get all files and folder info. Then show them on UI in a Grid or something.
You can have a download button for each file. You can use the code
How to: Download Files with FTP[
^] for getting the response stream. Then convert the stream to byte array and assign to the Response object for downloading in browser.
I found one example with similar concept -
A web based FTP client[
^]. But I don't guarantee, if it would work or not.
But you can work on the same logic to make it work with a little bit of research.