Les Parisiens, right on the border of the 6th and 7th, meets your criteria.
We usually go for lunch, because the lunch menu is a great value. But we had similar criteria to yours when we arrived on a Monday a couple years back and that was my dinner choice.
If you do go, I strongly suggest ordering the fish, which they do much better than the rest of their dishes.
I no longer find it as consistently fabulous as it was 3 years ago when we first went, but it’s usually good, and I’ve never had a bad or even “meh” fish dish there.
