What one language would you encourage Americans to learn, and why?
The language that they want to learn and would find the most useful to them.
Let's face it, English is the most-learned second language around the world because it is useful to just about everyone. There is no one comparable second language for English-speakers.
I think it would be ideal if some Americans learned Spanish, others learned Mandarin, and still others learned Arabic, Russian, Korean, and so forth.
But to pick one of those to be "the" second language for all Americans to learn would be a mistake, in my opinion.
I wouldn't. Multiple languages cause social disturbances (eg Quebec secessionists in Canada, Welsh speakers in the UK, Catalans in Spain, etc), inefficiency and confusion - what does it cost the EU to translate every doc't into 2 dozen (or whatever) different languages.
A much better solution would be to have everybody speak American.