Are there some fields where having skills in a language other than English is necessary to perform research at an international level?

Are there some fields where speaking a language other than English is necessary to perform research at an international level?

It depends on what you mean by "speaking" and "necessary". In mathematics, there is no need to speak any language but English and the language of the country you are working in, but there's a real benefit to being able to read other languages. It's not strictly necessary, and its importance varies between fields. In my case, I don't use other languages on a daily or even weekly basis, but probably read French on a monthly basis and German a little less frequently.

In my view, the reason for language exams isn't that these languages are required to be a researcher, but rather that they are helpful. The best argument I've heard for requiring language exams is as follows. Learning how to read mathematics in French or German is not very difficult, but it's still a burden if you just want to read one paper. Usually you can get around it by finding another exposition, finding someone to explain the paper to you, or just deciding the paper is not relevant enough to bother with. However, even though this is a rational solution to a one-time dilemma, it's a bad idea if you are going to be faced with these dilemmas repeatedly. At that point, you'll gain a lot in flexibility and convenience if you can read the papers you want to read. The purpose of language exams is to keep people from repeatedly making short-sighted choices.

I'd guess that language skills are more important in mathematics than in most scientific fields, because the mathematics literature has an enormously longer half-life. In my work, I frequently use and refer to papers that are 50 years old, and sometimes quite a bit more. These results have not always made it into textbooks, and even when they have the original papers sometimes contain valuable insights.

I'm going to cherry pick a bit.

In the area of robotics, the Japanese have one of the best journals and conferences (their journals were about 10%-20% acceptance rate about 3 years ago). Yet, many of those journals are written in Japanese. Here in Japan, students in robotics do not need to present their work at international conferences or journals, since they consider theirs good enough.

Many of the best robotics work in things like ICRA and IROS (from the Japanese) was presented in some form about 1-2 years ago.

That said, I do not think knowing Japanese is necessary for a successful tenure in robotics, but it certainly can help to have some competitive advantage.

In my field (mathematical physics), it is certainly true that most research is published in English, although there certainly is a non-trivial amount published in French, for example. Although being able to read French might not be required in many institutions, it still is very useful. I expect that for the other sciences the picture is similar (for the humanities on the other hand, I expect it may be very different).

Another issue however that becomes more important when looking for tenure(d) (track) positions are the teaching requirements. In many countries almost all teaching is done in the native language, at least at the undergraduate level. So it is important that you will be able to teach in this language, or at least be willing to learn the language in the near future.