Do you write them or leave them to your reader's imagination?
Is it necessary to write: "Excuse-moi, monsieur, but I am looking for the oh-so-charming Madmoiselle" if you have a Frenchman looking for his new love interest? Does he need to talk about her 'leetle shoes'? Does your Englishman have to sound like " 'ere, 'ere, guv'ner, tike yur boots off an' set yurself down hof' a mo'?"
I confess I have not done this, and my reasons are two-fold. Firstly, as a reader, I hate fighting through accents when the writer has put it all down phonetically. I can hear the accent in my head, I don't need it written down. Secondly, as a writer, I find I can give the impression of the accent through vocabulary choices and rhythms, if this is necessary.
North American: Sidewalk
North American: Bag of potato chips
English: Bag of crisps
There are regional vocabularies all over the world. I find using these words a far better indicator of the character's voice then plastering every word with an accent.
Tell me how you handle this situation. I'd be curious to know.
Y'all come back now, y'hear?
A heartfelt happy Fourth of July to all my American friends!