Scanning a ftp directory

[Frank Burton]

I have a website that has a folder with a few thousand files and sub
folders in it. I need to know the name of every file in this folder
and it's sub folders. The web server is a go-daddy linux machine and
my machine is running Mint linux. I have tried using an ftp client to
scan and generate a txt file for me but it only returns the top level
folders and nothing deeper. Google didn't really help me either. So I
am looking for any method that will work. I am willing to try
anything, be it cli, gui or a scripting language to get it done.
Thanks
Frank