We booked a small studio just behind the Élysée palace. It's a very safe neighborhood, actually you can meet more gendarmes than passers in the evening. The studio is small, but comfortable, exactly as described. It's not new, but it was very clean.
You can get a very nice sleep, as it is extremely quiet - it looks into the backyard of the building, no street noise at all. If I have to look for a downside - be aware that there is no elevator (it's only on the first floor though) and no view from the window. Also we were losing gsm connection inside. But the wi-fi was excellent.
Emma was our host and was extremely helpful for us. Everything was provided for our late arrival and even that late she called us to check if we were fine and sent us hints for the neighborhood. She then accommodated a late leave for us and afterwards after we managed to miss our plane from Paris, spent at least two hours late in the evening to help us find another place for two more days (a really hard thing to do in Paris). I can safely say that without her invaluable help, our stay in Paris would have been a lot less pleasant.