This question has no definite answer if time frame is not specified. The situation in 20s century changed very quickly. In the first half of the century, German and French dominated.
(More German than French). In the second half, it is clearly English, and one does not need any research to see this. But English dominates more and more. In the 1970-s and 1980-s about 1/3 of all papers was published in Russian. (I did count this. There was a Russian counterpart of Math Rev, using Cyrillic for Russian papers, so it was easy to count).
Not anymore. Until the late 70s, most German papers were published in German. Not anymore.
My guess would be that in 21st century an overwhelming majority of publications are in English, and there are some in French and Chinese. Proportion of other languages is negligibe.
EDIT. In the discussion, mostly arXiv is discussed, so you probably mean very recent papers. I follow the arxiv since its inception, and my impression is that less than
1% of all papers are written in French or Russian. I have not seen any in German or other languages, including Chinese.
EDIT2. One also has to specify what kinds of books and papers are we talking about. Of course, textbooks and lecture courses are published in every language. Because TEACHING in most countries is in the native language, especially undergraduate teaching. Same applies to many publications intended for more general audience, publications related to education and history, popular mathematics etc. In the arXiv they are in the sections "History" or "General math". All non-English papers on the arXiv that I know are in "History".
I will not be surprised if statistics from the arXiv will be very different from that in Mathscinet, even if one restricts Mathscinet to the recent years when arXiv exists. In fact arXiv is not a good representative for the whole mathematics. In some areas, almost all papers go to the arXiv, in other areas, only a small proportion.
EDIT3. OK, in Mathscinet they indicate the language:-) Since 2000:
70K in Chinese, 66K in Russian, 21K in French, 5K in Spanish and Japanese each, 4K in German and Italian each, 1K in Portuguese. Out of 1,358,623 total. Zentralblatt seems to have a similar feature but I could not make it work.