What is the best secondary language for an academic to know? Let's say someone young (~PhD student stage, possibly earlier) wants to become a professor. He doesn't mind moving around and will go wherever the best offer is. He'll obviously need English, but he's also motivated enough to learn another language. What is the best language to learn that will open the most opportunities?

If we proxy the number of jobs available in any country by research spending, then according to Wikipedia the most likely destinations are the USA, China, Japan, Germany and South Korea in that order. The main language in the US is already English, but the other four have local languages. However, I don't know how easy it is to get an academic job in any of these countries (or the ones later in the list - India, France, Russia ...) without knowing the local language. 

If the answer to this question varies by field, the I'm most interested in the sciences.
It depends on what kind of job we are talking about. For a PhD student, or for a postdoc, knowing the local language is not necessary in general. I know plenty of examples of people who got such a job without knowing any shred of the local language (in France, Switzerland, Korea...). The general expectation is that you make an effort to learn the language after some time, though. If only to have an easier time ordering food in restaurants and talking to your colleagues during coffee breaks.

For a professor job it depends more on the location. In some countries (e.g. Switzerland, the Netherlands, and many others) some classes are taught in English, so you don't need to know the local language immediately, although that is probably expected after some time. (In fact, I've been told it's a "disadvantage" to know the local language, because only lower-division courses are taught in it, and they are less interesting than upper-division courses.)

In some other places, courses are taught in the local language, but new professors get some teaching-free time (say, six months to a year) before being required to learn enough of the language to teach. (I know an example in Norway.)

In some other countries (e.g. France), you need to know the local language before getting the job, because teaching is mandatory in the local language. But I expect that if you are a good candidate, they will make an exception and arrange for you to only teach during the second semester, so you have time to take a crash course in the local language. But you would have to make it worth their while...

There exists some permanent or long-term research-only positions, all around the world (in France CNRS, in Germany Max-Planck...) It's often possible to get hired for one of these even without speaking the language, since you do not have the constraint of teaching.



In any case, it is impossible to give a general answer to your question. It is not helpful to look at global statistics, because a particular person is interested in getting a job in their own particular subfield. Which countries have the most jobs is not uniform. Even in "the sciences"...

But as you can see from above, learning a language in the hopes that it will land you an academic job is rather pointless. Your academic record is infinitely more valuable. You would have to be in an extremely specific situation for it to give you any kind of edge. Unless you have another reason to learn the language, I expect that your time is better spent on research. You will have time to learn the language later.

Also, most people don't approach the job search as "I'll take any job anywhere in the world". Most people have family, friends... that they like to see every now and then. If your whole world is based somewhere in Western Europe, will you take a job in East Asia or the Americas? Some people will, some people won't, especially if it's a permanent job. (Other make an effort for their postdocs.) So I'm not sure that you can approach this as "I'll learn the language where the most jobs are".



PS: it is not "obvious" that the person you are talking about will need English. In some fields, English is not the main language. For example in "history of [location]" the main language will probably be the language of [location].

PPS: Your Wikipedia link is about R&amp;D, not academia...