Let's consider a real historical example
Let's fix the historical period to the 14th century, and let's say that "language 1" is French and "language 2" is Romanian. Both French and Romanian are descended from Latin (which is thus "language 0"), and in the 14th century, they had had no contact for about 1000 years. No 14th century Frenchman spoke Romanian, and no 14th century Romanian spoke French.
But it came to pass that in 1396 a French army and a Romanian army had to join forces with a Hungarian army at Nicopolis (in the north of modern Bulgaria), to fight against the Ottomans. So how could the French and Romanians communicate?
First of all, it's absolutely clear that the top level leaders, for example Jean Le Maingre (marshal of France) and Mircea the Elder (Prince of Wallachia) would speak through interpreters. A great lord does not speak an approximation of a foreign language except in case of dire necessity.
Second, there was no time for them to learn the other language, although it was clear that the languages were related.
So, how did the interpreters communicate? Well, they had four possibilities:
Speak Latin ("language 0"). Both the French and Romanian armies had clerks who knew Latin, because Latin, although long dead, was used as a written language in diplomacy and administration. Of course, the French clerk's Latin would sound completely different from the Romanian clerk's Latin, but since the differences would be perfectly systematic they would very quickly learn to get over them.
Speak Italian, or actually, at that time, Genoese. The French had bona fide Genoese crossbowmen in their army, and there were Genoese colonies in Wallachia so that there were bound to be several Romanians who understood Genoese. (And anyway, the medieval opinion of Romanian peasants was that Italians spoke Romanian too, but quite badly.)
Speak Greek. Greek was a language of culture. On the Romanian side, there must have been traders or churchmen who spoke Byzantine Greek; the French must have had one or two priests who understood Common Greek. The differences in pronunciation would be even more marked than the differences between the pronunciations of Latin, but they could still be overcome.
Use Hungarian interpreters. The bridge power at that time was Hungary, whose king, Sigismund, would eventually become Holy Roman Emperor. The Hungarians maintained diplomatic relationships with both France and Wallachia, and thus had people who could speak French, and people who could speak Romanian, and, with a bit of luck, maybe they had some clerk who could speak both French and Romanian.
The technical question is how to make sure that the characters understand each other without troubling the reader. This is quite interesting because the story, as far as I understand, is to be written in English for an English-speaking audience.
Let's assume that the story is to be written from the point of view of a character from population A, who speaks language 1, which will be conventionally represented by English. So the question becomes: how to represent a language similar enough to English and still different enough, so that the readers will perceive it as a foreign yet closely related and understandable language.
Now, if this were a story written in Romanian, it would be easy: let language 2, the language of population B, be represented by Italian; if the author chooses the Italian phrases carefully Romanians will understand them, and yet they will clearly be in a foreign language. Or if the story were written in French, language 2 could be represented by Middle French (the language of Rabelais); with a bit of effort a French reader could understand Middle French -- after all, Balzac wrote an entire book, Les contes drolatiques, in mock-Middle French, and it is still in print (and hilarious). Or if the story were written in Russian, language 2 could be represented by a Russian recension of Church Slavonic.
But where can one find a language clearly related to English, foreign enough to confer an air of difficulty, but close enough to remain intelligible? My suggestion is to represent language 2 with a slightly modernized Middle English; it may be that my view is prejudiced (after all, English is so much unlike my mother tongue that for me the differences between Middle English and Modern English seem quite small), but I believe that slightly modernized Middle English would be intelligible, with a little effort:
'Wepyng and waylyng, care and oother sorwe I knowe ynogh, on even and a-morwe,' quod the Marchant, 'and so doon oother mo that wedded been.'
which in Modern English would be
'Weeping and wailing, care and other sorrow I know enough, in the evening and in the morning,' said the Merchant, 'and so do many others who have been married.'
(Chaucer, The Canterbury Tales, as quoted and translated by Wikipedia.)
Of course, it should not be overdone. A phrase here, a sentence there, a few words from place to place ought to be enough to convey the color. The story should remain a story written in English; use the stand-in for language 2 sparingly.