This clip is from his movie, G.I. Blues, and the song is Wooden Heart. If it sounds familiar to German speakers, it's because the melody is the same as the German folk song, "Muss i denn, muss i denn zum Städtele hinaus" by Friedrich Silcher. To anyone who didn't sing that as a child (i.e., anyone who didn't grow up in Germany, with German parents, or learning German), that's the song he starts singing in German at 1:06.
Both are love songs, but they don't quite have the same meanings. The folk song is about a guy going away, telling his girlfriend he will stay true to her, and that if they are together after a year, they'll be married. Wooden Heart is more of a "don't break my heart" than a "I won't break your heart." I guess Elvis sang plenty of other songs asking women not to break his heart. Someone posted a good translation on a forum if you're more curious.
Some of the pre-production filming for the movie was done on location in West Germany while Elvis was stationed there in the Army. I'd recommend watching the full film if you can find it...not just because I absolutely love Elvis and would almost always recommend him.
Alles gute zum Geburtstag Elvis!