When it comes to linguistically singular nations (France, Britain, Prussia), officers would speak the language of their nation (French, English, and German respectively). These nations were bound more by culture and crown but still had singular languages with dialectal variations that caused few if any issues.

Austria is a particularly interesting issue due to the nature of her Empire. Austria was a multiethnic Empire that legally had laws in German and Latin. However, due to the restrictions on officers coming from the nobility (thereby being German or German speaking), Austrian officers would speak German to each other in command and need translators for speaking to their NCOs (whom might know German) or the rank and file.

Russia was also a multiethnic Empire that defied a singular language. Rather than being tied through a court language, the Russian army was a mess of foreign officers that would speak French, German, English, Polish, Swedish, Turkish, Arabic even, and of course, Russian. However French and German were the main language of many Russian nobles and this would be the main language.

The oddity is France despite being made of French speaking Officers. The French army was a truly multiethnic army that composed of French, Italian, German, and Polish soldiers yet still was staffed with French speaking officers. As a result, French officers that knew foreign languages were at a premium, with Frenchmen that lived on the borders or grew up there (like Michel Net whom was born in what is now Germany).

Overall, it always ended up being French and German. As most of the nobility of Europe spoke and/or read French as it was the source of culture before the Revolution, French was an easy go to language. Conversely German was a geographically diverse language that stretched from the borders of France to the Baltic (many Baltic Germans served as officers in the Russian army).