My approach is come up with a number of ways the language differs from the other languages - genders, sentence structure, pronouns, prepositions, formal/informal modes, sounds etc - and then note it in passing.
"Like others from his culture, he had difficulty with the genders of our words, often using the wrong pronoun or adjective." or "Like most of his kind, he couldn't pronounce 'B' properly and it sounded more like a 'P'." or similar.
Perhaps occasionally I might have unusual phrasing that is a "signature" of the speaker but not to the point of Yoda-Speech.
I've got a German friend who invariably says, "we've got to get together over a few beers and tell us gossip."
And a Chinese friend who always states figures like "it cost me a hundred over dollars".
Another Chinese friend had extreme difficulty with our pronouns and would say things like "I'm going to my friend's house, he is going to loan me her computer".
All of these things are due to core differences in the languages - Chinese does not have sex-differentiated third-person pronouns, German word order differs from English.
A native French speaker would find German's extra gender problematic as (s)he would have his/her own ideas on what gender an object should have and it's highly likely that the same object would have a completely different gender in German. An English speaker has to learn what gender a word has in German, a French speaker has to "forget" their own gender assignments.
There's tons of scope for coming up with differences between languages which you can then render in English and note the difficulties in the text.
"He spoke very slowly, struggling to get the word order and tenses correct. Why did Fribknull have to be such an accursedly complex language?"
Or even: "He loved Gadath, it was so much simpler than his own language."
If you want to play, you could always interject unusual words in place:
"'Please pass me the elephant', he said. The others at the table laughed loudly and, knowing what he'd meant to say, K'pull passed him the salt-shaker."