IMHO this strongly depends on the subfield you are in. In mathematics it would be probably fair to say that such a second language is French. I am not an expert but I guess Latin still does play quite some role in the life sciences and the law.

Quite naturally, if one studies some localized phenomena (endemic species, local communities etc.) then the language of the country in question (and/or perhaps a local language, if different from the country's official language(s)) would probably be an appropriate second language to go for.

Mandarin Chinese but not for long.  English is now established as the lingua franca in science and the internet will keep it so.  Most scientists in the future will consider English a crucial skill and many do already.

The glorious wealth of other languages will be unaffected by this is cultural terms however.

Two are the ways:

(1) the whole world [of us, as customers of industrial goods, also the "scientific" ones] will be relating each other in one language only [that is English],

or

(2) the matter of the different languages will loose its cruciality. Not any longer.

As translation is the final hinge for AI process and machines to reproduce the human relations, and a stratospheric number of investors is pushing the industries to there, and we humans are the ware for the machine of industrial consumption (also of industrial production of science, healthcare, education, thus graduations, publications, etx.), it will be not possible not to have one output only, (1) or (2) coming out from the fork.

Necessarily, I think all kindo industries will prefer the easiest route — that is the 2nd one: our embodied devices will translate us — our voice, or readings — in real-time.

Conversely, humanly [our inner, private, secret or informal speech] we will prefer the more complex way, the 1st: some common way to talk / write a bad English, bad Spanish, ungrammatical German, more and more approximate Chinese, roughly Arabic, chewed French and dialectal Italian, will spread through the streets, mostly assented as "normal" or "simpler", natural for every (not impolite, of course, but… yes: shallow) human non-assisted by AIs relationship.

Multi-language.

Remember The Mézga Family, and Aladár's idea to inject a plasma into the brain to learn passively a new knowledge all at once?

Cartoons usually anticipate Science by ~30 years on some issues, but then Science solves the same problem in another way.

https://www.youtube.com/watch?v=0aEuipbe6dg

Spanish, Arabic, Chinese, and Russian are other widely spread, culture universal, languages.

We should look to the philosophers of the past to understand why need a language of science.  Ibn Sina the great scientist and philosopher was Persian but wrote the majority of his works in Arabic because it was the universal language of the Middle East.  had he written it in Persian it would have been unlikely to have had the impact on both Arabic and European philosophy and science.

Giuseppe, you made me think about the new "real time translation" tool that is been applied by Microsoft with Skype. This would be the perfect scenario. A place where you could just write in your own mother language and then a software would perfectly translate it into any language. But so far, besides English, I think Mandarin is the way to go, at least regarding biological sciences.