One idea I've heard from time to time is that if we all spoke one language, we wouldn't have war any more.
I can think of counter-examples to this. For example, the invasion of Kuwait by Iraq (both Arabic-speaking) as an international war, and countless civil wars such as Somalia.
However, does sharing the same language play any role in the likelihood of war, either by decreasing or, perhaps counter-intuitively, increasing it?
Generally speaking, the answer is no, sharing the same language doesn't play a sound role in the likelihood of war.
Richardson's (1960) Statistics of Deadly Quarrels provides the earliest systematic treatment of the impact of cultural similarity on international conflict. Analyzing more than 300 wars and disputes from 1820 to 1929, he finds that, in the main, common language did not predict either increased or decreased bellicosity among warring parties (pp. 223-30). However, for the major language groups that he studies (N = 13), Chinese dyads tended to be less war prone, whereas Spanish dyads were more likely to fight one another. Contrary to the belief of the advocates of universal languages, such as Esperanto, that common language across states would increase the likelihood of peace through more effective communication, similarity or difference in language between states seemed to have little effect on the occurrence of war. (cited from Errol A. Henderson, Culture or Contiguity (1997) [1])
Most of the contemporary conflict studies prefer investigating the effect of ethnicity on the likelihood of armed conflicts, and though ethnicity and language are strongly related to each other, ethnicity is believed to be a better explanatory factor than any merely linguistic factors.
Nonetheless, the importance of language as a means of communication and as an identity factor makes it a convenient instrument of propaganda both for conflict escalation and for conflict resolution. For conflict escalation, Ranko Bugarski [2] investigated Yugoslavia's case,
stressing the close connections between language and nationalism and showing how language played different roles in the events leading to the disintegration of the federation and warfare on its territory.
Paul A. Chilton [3] offers a broader theoretical discussion of the role played by language and discourse in conflict resolution, focusing
on the issue of who talks to whom (or who is permitted to talk to whom), and, on the other hand, the practices in such communication that contribute to or impede conflict or its resolution.
[1]: Henderson, E. A. (1997). Culture or Contiguity: Ethnic Conflict, the Similarity of States, and the Onset of War, 1820-1989. The Journal of Conflict Resolution, 41(5), 649–668. http://www.jstor.org/stable/174468
[2]: Bugarski, R. (2001). Language, Nationalism and War in Yugoslavia. International Journal of the Sociology of Language, 2001(151), 69-87. https://doi.org/10.1515/ijsl.2001.048
[3]: Chilton, P. A. (1997). The Role of Language in Human Conflict: Prolegomena to the Investigation of Language as a Factor in Conflict Causation and Resolution. Current Issues in Language and Society, 4:3, 174-189, https://doi.org/10.1080/13520529709615497
One well-known source of this idea is Dr. Zamenhoff, the inventor of Esperanto language, who indeed believed that most conflicts, including the armed ones, originate from misunderstanding:
Zamenhof's goal was to create an easy and flexible language that would serve as a universal second language to foster world peace and international understanding, and to build a "community of speakers"
As mentioned in the comments by the @LateralFractal, this is closely related to the Sapir-Whorf hypothesis (aka Linguistic relativity), which essentially suggests that language determines the way we think and the other way around. Note that in Linguistics this view has been largely supplemented by the Generative Grammar approaches, which suggests that all the languages share the same underlying structure, likely hard-coded in human brain.
The argument ultimately boils down to whether the wars results from decisions or viewpoints of particular personalities (or peoples) who cannot agree with each other OR whether they result from the underlying structural conflicts, like getting a hand on natural resources, pushing competitors from a market, gaining independence from an oppressive regime, boosting arms sales, etc. One recent incarnation of such thinking is, e.g., dismissing "Russian psyche/mindset", as unjustly suspicious of other people's intentions - suggesting that the western politicians are motivated by high goals, such as peace, human rights, exterminating poverty.
If we understand language as a common discourse and shared cultural references, I believe that the likelihood of war will be significantly smaller. In the modern era, I can't think of a European war between nations who shared the same language. Perhaps the likelihood that such states remain independent is also smaller. I think of the 'Anschluß' on the eve of the 2nd world war.
The American independence war took place when American culture was already several centuries old and the British lived in a different cultural realm.
Interstate wars between formerly colonized nations (such as the terrible La Plata war in Latin America) are an exception, but generally, I claim that speaking the same language in the fullest sense of shared cultural references, does decrease the likelihood of war.
Here is a map of the neighboring country's language: https://www.mapsofworld.com/world-language-map.htm
Here is an interesting update on the Richardson study: "The one social factor that does have some detectable correlation with war is religion." https://pdfs.semanticscholar.org/6e9c/de40cb861ac28c735748837650b9a40425d9.pdf
