In French "marié" is the word for "married", and yes, it affects the pronunciation - "ma-ree-EH" or as we'd say it, "ma-ree-AY". It's certainly not a name in France. I think it also means 'spouse'. I'm not French but I'd say it like that else why would the accent be there? I'd stick with "Marie", the accent will probably only cause confusion.
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