To me, a perfect vacation day includes visiting lots of places, eating lots of good food, and coming away with different local experiences. PERFECT = VARIETY. This rule applies even when traveling with young kids. And with a big city like Paris, France... there will not be any problems meeting all these objectives.
I recommend finding a hotel near the Eiffel Tower. It's such an awesome feeling to exit the hotel, turn the corner, and then look up to find the Eiffel Tower staring right at you. The Metro and RER stations are nearby, as are lots of restaurants, cafes, and bakeries.
Here is our suggested itinerary for the perfect family vacation day in Paris with kids: