The 1000 Genomes FTP site is available as an end point in the Globus Online system. In order to access the data you need to sign up for an account with Globus via their signup page. You must also install the Globus Connect Personal software and setup a personal endpoint to download the data too.
The 1000 Genomes end point is one of several EMBL-EBI hosted end points and is called ebi#public and the data is found in the 1000G sub directory.
When you have setup your personal end point you should be able to start a transfer using their web interface.