When you load the launcher, it will detect that you should be playing on the EU megaserver and do you want to migrate to that now.
CLICK DECLINE and DECLINE again, otherwise you will download the entire game again.
After you have clicked decline, go to "x:\xxxx\Zenimax Online" (xxx is where you personally installed it) and check you have the folder called "The Elder Scrolls Online" and its 30gb in size.
Then just copy and paste it to the same location. You will get 2 folders then "The Elder Scrolls Online" and "The Elder Scrolls Online - Copy". Now all you need to do is rename "The Elder Scrolls Online - Copy" to "The Elder Scrolls Online EU" and reload the launcher.
If it asks you to migrate DECLINE it again, it'll download a small patch and then your done.
To check your game is working OK, click the cog wheel in the top right, make sure it says your on the European Megaserver. Apply and click play.
Enter in your personal details and it should say it can't find any servers. This tells you your client is fine.
If your concerned you can run the repair tool to check your installation too. The above process i followed and mine is working fine.
Also BTW its running a really up to date client. I think they are throwing everything at us this beta.