If you have ssh access there are several ways to do this, but since you say you have ftp access, Voce can access from most modern browsers, just put the ftp address in the browser address bar, for example:
ftp://meuftp.com.br/
You can also use Fireftp to, ay yes, manage an ftp via Firefox, or the sftp, through the Chrome.
You also have the option to use an FTP desktop program, there are several, I will indicate the Filizilla pq is easy to use and is cross-platform.
Edited | Device Sharing:
A good alternative (FREE) for backup is the Crashplan, Voce installs on your device and they all start to share the files that Voce determine, of course for that Voce needs to be able to install on a provider, if you want the files to be stored on your disks.
CLICK TO DOWNLOAD THE CRASHPLAN.
What is the server environment? Linux? Windows? Voce has shell access? has root access?
– Sidon
godaddy server environment is linux with Cpanel. Yes, I have shell access. About root, I do not know inform.
– John Joe
For backup, on linux, I would use rsync, but Cobian is a good choice. My answer below does not suit you?
– Sidon