It's impossible to "change" language in Diablo 3 without hassle, as in most of Blizzard's latest games, as in.
This requires the least data download, since it only downloads the necessary language files.
Go to Options -> Account
Choose a language from the dropdown. The launcher will start and download the missing language files automatically.
This is clearly the long road, since it requires you to download the whole stuff in any particular language.
You will have to download the appropriate client from Battle.Net, to which you have access from your account. All EU accounts should have access to english, though.
Then you will have to uninstall the game and install the new client.
Log in to your Battle.Net and check out the downloads section.
The download will set you back about 7 GB and will per default not overwrite other downloads, since it has the locale code in its directory name: e.g.
Here is what my account looks like: