I've walked all over Paris in ballet flats, streamline sneakers (that look like ballet flats) and sandals. I have really high arches and felt best when I had plenty of arch support. The sandals went with me through the Louvre (we took the train to get there). I recommend wearing your most comfortable shoes to the Louvre. I think I walked at least 3 or 4 miles just inside the Louvre and I did not see everything. I might have seen 20% and I was there at least 4 hours.
We also walked from my B&B which was one block from the park where the Eiffel Tower is over to the Musee d'Orsay and back. Paris is definitely one of those cities where you don't realize how far or how much you've walked because there's so much to see on the streetscape. I think I only realized how much walking I did when I got back to my room and only wanted to sleep.
Overall, my streamlined sneaks worked the best for me - because they had arch support and I was able to look stylish without whipping out the athletic shoes for cushiony support.
BTW I was there in late July early August.