Even though English is the de facto academic lingua franca in the West, I'm sure there is still ample amounts of history written in other Western languages, let alone nonwestern ones. The vast majority of this history goes untranslated, whether its in Italian, Arabic, or Mandarin, and is therefore inaccessible for most historians who do not speak those languages. Do historians who only speak one language go out of their way to examine historiographical developments?
Frequently, at least in ancient studies, scholars are expected to know modern research languages as well as the relevant ancient ones, and frequently big chunks of untranslated text just show up. As an example, I wanted to look something up in the CDLI (database of cuneiform texts); double-checking their typology page for the list of Royal Inscription publications jumps right into four paragraphs of French, before a sentence or two of English. Its a very 19th century mindset still in many places, and the size of the field reinforces this--journals and publishers don't feel much pressure to move outside their comfort zone.
There is a heavy, heavy western European bias, especially without the competition of Soviet scholars to make Russian a big player. For Assyriology, there is a lot of good scholarship being done in Iraq (especially archaeology, both because of the obvious locational benefits and impressive institutions), but much is published in Arabic and makes a lot less impact, or a lot slower impact, than it should. For scholars wanting to work outside of European languages (or Arabic, maybe), there is limited opportunity. This makes developing a community of scholarship in that language much harder, reinforcing the lack of 'need' for Western researchers to engage with that language/community. The Finnish scholar Simo Parpola is foundational in Neo-Assyrian studies, and has taught a number of prominent Finnish students, but all publish almost entirely in English (not exclusively; German is also notable).
In sum, the structure of the field, rather than any single person, excludes languages from outside Western Europe, and only those who are working to make journals and universities more open to these contributions have yet to turn the tide.
In my experience working with foreign sources, most historians will try and get at least reading fluency in a language. Since the majority of sources are written, there's little issue with slowly working your way through a source with a dictionary in one hand and a grammar guide in the other. However, language selection becomes a larger issue here.
It is also my experience that historiography in languages outside of the obvious ones is rarely if ever considered. If you are writing about say, Belgium, you'd read sources in English, French, Dutch and German. But you are unlikely to browse Japanese books for Belgian history. This may be different in non-European history, but in European work, the languages consulted are usually the local languages and English/German/French, these days heavily leaning towards English.
Generally historians writing in other languages will also gauge what language is most relevant. While I could in theory write a book about Spanish California in German, the question I'd ask myself is what would that achieve? If I want to reach a larger audience, I need to write in a language people will read. For better or worse, scholarship is largely done in English, even by non-Anglophone historians.
Now I can't talk about non-European history as I am a European historian by trade, but most committed historians in my experience, regardless of field, will consult the local languages. If you are studying ancient Chinese history, it would be foolhardy to not consult Mandarin sources.
So while I do think it probably does occur, at least in my field and in my experience, historians know their audience well enough to gauge what language(s) it would be prudent to do research in.
Historians are generally expected to have sufficient proficiency in the languages relevant to their subfield to engage with both source material and scholarship in those languages. You can't really develop specialized knowledge in a field if you don't have the requisite language skills to engage thoughtfully with the work that's being done there, and you can't do research without knowing the language(s) that your source materials are written in.
Most Ph.D. programs require their doctoral candidates to pass an examination in at least one foreign language (usually two for European history and probably most other non-Anglosphere fields). For example, in my case, I had to pass exams in Romanian and German. In my experience, for Europeanists, there also seems to be a tacit expectation that you have some reading ability in French, so I had to invest some of my own time into that after I started my current research job.
Of course, there are cases where it's not practical for historians to know every single language relevant to their work; for example, I don't speak much Russian and I don't speak Hungarian or Polish at all. In cases where material in e.g. Russian isn't translated into English or German, it does become a problem and it's a time consuming slog to get through it, which is why I'm working on improving my Russian skills on my own time. You can't be an omniglot, there's only so many hours in the day, but if you want to research in a field, you ultimately have to be willing to put in the time to learn the relevant language(s).
In my experience in medieval studies, in grad school we had to pass three proficiency exams, in French, German, and Latin. The Latin exam had two levels and was famously difficult; the French and German ones are less tortuous, but they're intended to make sure we can read academic literature about the Middle Ages in those languages. English, French, and German are the most usual languages of scholarship for the Middle Ages, and the Latin is so that we can read stuff that was actually written in the Middle Ages.
On top of our other classes and writing our dissertations, we were also expected to learn any other medieval and modern languages that would be useful, either formally in a class or on our own. My school was big on Celtic languages and Old English. Personally I took Old French and Arabic since those are really useful for the crusades.
Basically that means I can work with medieval things written in Latin and Old French, and I can read modern scholarship in French and German. Thanks to French and Latin I can stumble through books in Spanish and Italian too (also significant for crusade histories!). My Arabic is pretty terrible so I can't really engage with Arabic scholarship as much as I'd like. There definitely is a lot of that!
I know there are lots of interesting things written about the crusades in Hebrew, Danish, Russian, Polish, Czech...I can't read any of those either, but fortunately historians who work in those languages usually speak English as well, and often publish in English too.
So, as native English speakers, we're strongly encouraged to learn other languages (at least, we were at my school), and non-native English speakers tend to learn English. For the crusades/medieval history, we're all pretty well interconnected.
Field: Medieval Islamic History
Language of primary sources (only Middle East):
Classical Arabic: You must know it. It grants you access to sources from the 7th to the 19th century, for contemporary studies on Islam you have to know Modern Standard Arabic but usually both the variants are studied at uni so it is not really a problem. Classical Persian (10th-18th centuries): optional but if you study Islam also from the 10th century on you will feel the need to access the sources in Persian because from this point in history the production of knowledge in the Islamicate world becomes highly persianised. Ottoman Turkish: only if you are interested in later periods of Islamic history and specifically Turkish history. In this case you must know both Classical Arabic and Classical Persian.
Other useful languages but not required are dialects of Aramaic or Greek that grant you access to Christian sources. But usually you can find translation in European languages made by specialists of those languages.
Language of secondary sources:
Arabic, English, French and German. English is just a must. French and German are also really useful languages in this field and for some specific topics you have to know them. If you study Ottoman history you have to know also Modern Turkish because there is a big production of knowledge in Turkish in this field.
For all intents and purposes it really is beneficial to have knowledge in multiple languages when it comes to academia.
Just to offer some examples, I focus on Buddhist studies, and if I choose to go down the graduate and post-graduate path, I would benefit tremendously to learn Classical Chinese, Sanskrit, some Pali, and Tibetan. Then there's the contemporary scholarship from around the world that studies the subject. Take Dunhuang and silk road studies for example, there was such a significant historical and international presence and interest in the art history of the region, that there's a major international collaborative project, teams from not just China, but Japan, Germany, Russia, France, Korea, the UK, America, working on cataloguing the sites and translating texts. It's the same for other fields. One of my college professors who specializes in 20th century Chinese, Taiwanese, and Chinese diaspora history, lamented that not enough CCP historians that speak French of Russian, which are crucial to understanding the early developments of the Chinese Communist Party and their international interactions.
Indeed, there are levels of ignorance from simply not knowing what historiography may be developing in other countries. It's important to then read from scholars who are multilingual, who have covered the literature from many different countries, and to at the very least have that basic understanding. You can get a sense of that by going to panels and speaking to other fellow scholars of the field. At the end of the day though, it would be best to acquire knowledge in more languages, and hey, there are benefits to that beyond academia!
Historians working in a field try to learn both the languages of the primary sources and the relevant languages in which secondary studies have appeared. Thus a historian of modern Egypt would know Arabic for the Egyptian primary sources and would also typically know English, French and German for secondary sources. Usually, however, it is the Egyptians themselves or scholars from countries with a big area-studies establishment that produce such history-writing, and they have the density of training, specialists and conferences to allow them to do innovative work. If you think about it, it is seldom that a one-off book in e.g. Bulgarian would reconfigure a historical field somewhere else in the world. It is always possible that important studies might appear in other languages such as Turkish, Russian and Japanese, but if they are sufficiently important they typically get translated either into English or French or into Arabic.