I've come to think of speech and mannerisms as a single subject. People have a way of communicating, not just of speaking, that is unique.
Think of people you know whose communication styles jumped out at you.
There's an accountant who used to work with my husband who, if you asked him how he was, always answered, "FAN-tastic!" (Happiest accountant I ever met. Weird.) I used to work with a woman who ended every sentence with a trailing so. "I made some fresh coffee, so..." "I put more paper in the copier, so..." There's a young woman my son is friends with who has an anxiety disorder and, when not walking, either picks at her fingernails or chews her hair. Her hair and nails are always a mess. Have a character who constantly swears... that's a gimme, we all know that guy IRL. Or maybe everyone in your comic swears and you add the one guy who never does. I know a young woman who stares at the ground when she speaks to you. An old woman who grips your arm whenever she talks to you, and you wonder if you're going to get a bruise. Or you can have a character who's always drunk and slurring his words, or always SHOUTING, or hath a lithp... etc. etc.
Edit: I am hereby guilty of answering your TITLE, and not your post.
To answer your actual question, I wouldn't write the accent. I'd grab the words that were different in the two languages and use those and other things like wardrobe to indicate the difference.