Okay, now it's in English and the intro scene is not missing anymore.
It's a little odd, though that I have to change the Origin Client Language to determine which version of a game I want to be playing. EA should actually ask me before installing or - even easier - allow me to just choose it from the game's options. You know, how it was done back in the days...
The way I had to do it required a complete re-download (10 GBs) and reinstall of the game.
Thanks to Kuro for helping me out here!
EDIT:
By the way, the issue with the missing intro scene when switching to English must have occured, because I was messing with some of the game's registry values at first to change the language from German to English. It worked flawlessly with some other games that required me to do so, but obviously you got to be very careful / exactly know what you're doing or otherwise you might screw up the entire installation.
Well again, this is why I highly request that developers/publishers go back to simply let users choose the language from the in-game options ;-)
Because what's the point of buying/installing a multilingual version of a game when the language you get is restricted to Geo-Targeting by default?