You may not be able to write your story in a different language, but you can drive home the point that they are speaking a different language by making the language part of the story. For instance, an easy one is to have two words that are not at all related in English make a pun in another language. (In the English and accents of Shakespeare's time, "loins" and "lines" were pronounced essentially identically, so the line in R&J, "From forth the fatal lines of these two foes..." is a double entendre. I am reminded also of a joke, I think in Babylon 5, which a character tried to explain to the others, which depended on the similarity in his language between the word for spiritual enlightenment and the name of a small species of fish.) Also, a fictional language might have two or three words which make subtle distinctions between things English labels collectively. Legend has it that the Inuit have words for every different kind of snow, and the Ancient Greeks had words for every different kind of love or affection.
You can go beyond that, though. Think about languages other than English which you have studied, even a little bit. If you know how Latin works, or the other Romance languages, or Greek or German or Japanese, then you have models--not for creating a whole new language, but at least for having an idea of how the language your characters speak is different from your own, and what features it might have. Is it lyrical and flowing, like Italian, or guttural and staccato, like German and English? Does it mark gender, declension, tense, number, etc. with endings, like Latin and the Romance languages, or using particles or phrases, like Japanese and English?
(If I want to say "George's book," in English or in Latin, I convert George from the Nominative, for use as the subject of a sentence, to the Genitive case, indicating possession, by changing the ending. In English, George becomes Georges, which we shorten to George's. In Latin, Georgius becomes Georgii, giving us "liber Georgii." Literally "book of George," or "book belonging to George." In Japanese, a particle, rather than an ending, is used to mark the function of the word in the sentence. It would be something like "Jioju o hon." And where a word serving as the subject of the sentence lives in its nominative form in Latin, i.e. Liber, in Japanese the subject--or rather the topic--of the sentence is marked with another particle. "Jioju o hon wa..." ...which you might translate literally as, "Regarding George's book...")
The effect of all of this is that languages have different... talents. Some languages rhyme easily, like the Romance languages where practically everything ends in a vowel or some other set ending, because a limited set of word endings are used to mark how words are being used in the sentence. If all of your words are going to end in certain endings marking plural, singular, past, present, masculine, feminine, then the frequency of those same ending syllables makes rhyming easier. If words frequently end in vowels, the language will be more lyrical and flowing as well, leading to the invention of operatic singing styles. If the language is more guttural or staccato, that might cause other kinds of music, perhaps instrumental, to be more prevalent than operatic arias.
Or, it might be something simple but crucial. In a D&D (technically, a Pathfinder) campaign I played in, we decided we would use real-world stand-ins for all the game languages. Latin would play the role of Common, Ancient Greek would play the role of Celestial, and various modern languages would play the roles of the vulgate tongues. For instance, one character decided that his character's homeland had a Germanic feel, so whenever it became relevant that he was speaking his native language, we would use German as the stand-in. (I think we used Tolkein's Elvish for Elvish, though.) One of the big ways this played out was in messaging spells with word limits. Latin has no articles, and you can roll most pronouns into their verbs (similarly to Spanish) so, "He is going to the Forest of Beasts," might be simply, "Ad Silvam Bestiarum eat."
Your languages aren't real languages, so you don't have to learn them, and you don't have to invent them. But seeing how different languages work in the real world may inspire you as to how these fiction languages, in their differences from English, allow for small details of your story that drive home the point that they are speaking a different language without you having to actually represent that language. If you narrate that a certain joke works for a certain reason, or a certain line of poetry works for a certain reason, or a certain idiom works, or that two words in their language sound alike and could be mistaken for one another, or what have you, you've gotten the best world-building aspects of a fictional language without having to actually create one.
