Would Restaurant Pompette work budget-wise for you?
If that doesn’t work, perhaps look at DaiLo, one of the more interesting restaurants in the area in my opinion and the room is never loud, esp. if you ask for a booth seat.
Another option might be Le Baratin, solid neighborhood bistro feel, and probably more budget friendly than Pompette. But for the price, you could do a lot worse than Le Baratin.
