Learning their language is most always a winner, and has saved me in most circumstances on Germany where somebody didn't know English. (I've already told the story of my big failure, so I won't repeat it.)
And you're correct, English is strongly rooted in (earlier) German; add some Latin (the Romance languages) and you've got most of it.
Gaelic has a few contributions too. The British word "smashing", meaning "good", comes from Gaelic "'S math sin!", pronounced "ss-MAH-Sheen", direct translation "That is good" in the sense of "That has the inherent attribute of being good."
Don't ask me about the (rock?) group named "Smashing Pumpkins." I smell a bilingual jest.
Most of the Germans I met spoke English and at the time, it was required in school, so I always had help. If I was stuck with a word or a meaning, I was gently corrected. And one woman told me, "We all speak English, but we want you to speak German. When we come to America, we will speak American." And they made a distinction between "English" and "American"...
A lot of times, the only differences between the American and German words was the spelling: bier - beer; baer - bear, or the pronunciation.