To get a detailed update log from the launcher; please open the Elite Dangerous Launcher and, from the Options menu, check Detailed Update Log. The Options menu is found in the upper right of the Launcher.
Once you have done this please close and reopen the Launcher and retry the download.
If it fails again then please open a support ticket (using the button below) and send us the Update.log file. Possible locations of this file are listed in this FAQ.
Once we have this we should be able to take a look and see how we can help you download the game.