I think the most dangerous parts of Paris are the very touristy areas during busy times. Pickpockets and such prey on tourists. December is a low season, so it won't be that bad. On the plus side, she will be able to enjoy the Christmas Markets. Vin Chaud + Tartiflette = very happy jtfrogger.
In our last trip to France, we spent one night at
Hotel Fontaines du Luxembourg. I would recommend it as a nice hotel for a reasonable price. The neighbourhood seemed fine, but we were only there for one day.