Micky, the core touristic Montmartre district is quite safe. That is basically the central area with anchors showing tourist places shown at
our page. If you look to the right of this area on the map, you will see the Boulevard Barbes and Chateau Rouge metro station. That is the ethnic district people may talk about. Skip it at night as you are alone. Altogether, in Paris as in all touristic cities, don’t look too much as a tourist with your purse, phone and camera highly visible. You may be robbed. In general, be cautious. Nothing more. You should not be worried.