Admittedly, I don't write a lot of characters that don't speak my dialect. The trick is to do it in a way that is both convincing, interesting, and easy to read. There was a Scottish character in an RP that was played by an actual Scottish person. He wrote a paragraph or two entirely in scots, and was proud of the fact that nobody in the RP could read it, and google translate couldn't properly decipher it (but it did get you close). What's the point?

The truth is that most people who don't have English as their primary language may pronounce words a bit differently, but the sentence structure more or less stays the same. It's hard to make those odd sounds come out in text without misspelling the word, which I don't recommend. That's why I choose to substitute certain words or phrases with words of the character's primary language. A french man who's confronted with a perilous situation might say "Oh mon due!" (oh my god) or "Sacare bleu!" (sacred blue!) Both are common french "cuss words," and can add a little flavor to your character's dialog. The french also have a system where their nouns are denoted with a sex. Le for masculine nouns, la for feminine nouns, and les for plural nouns. So someone could say "You hit le hand!" and become decidedly french while doing it. Do make sure you're using the correct prefix if you decide to go this route. Lastly, you can observe the things that people with different primary languages struggle with. The french don't actually say "turn on" in their own language, but "open." My Canadian-French friend will occasionally ask you to "open the lights" when she walks into a dark room.