Which second language should an American homeschool teach? Here, not necessarily in order, are some suggestions along with why I recommend them.
American Sign Language
I have a number of Deaf friends and find ASL to be a beautiful language. Yes, it is a foreign language, not to be confused with SEE (signed exact English, which was invented by hearing people.) ASL has its own grammar and syntax; if you master it you will have mastered a second language. Most universities recognize this. Ideally you will learn ASL from a Deaf teacher (a native "speaker.")
German
German is an academically important language, and the second most spoken language in Europe. Germans have a long written history, making it a great language for anyone planning advanced studies in theology, psychology, science, or mathematics. It is also an important language for classical musicians. As a bonus, the vocabulary is easy for native English speakers.
Spanish
OK, editorial comment here. I have never learned Spanish simply because as an American I feel it is being imposed on me. Our own Deaf citizens are expected to learn English, a language they cannot hear, while hearing people enter the country illegally and get to "press 2 for Spanish." Other than knowing what everyone in line at the DMV or Wal-Mart is talking about, the only reason I would choose to learn Spanish is to read Don Quixote in the original language.
Others
One of my sons is learning Russian as a minor to go with his computer science major. If your family lives in New England, French would facilitate trips to Quebec. If you have access to a native speaker of any language, why not learn that language? Any foreign language study develops your thinking skills and expands your understanding of the world.
Choose a language and enjoy it!