If you want to enjoy a rather spectacular view of Notre Dame, free from the maddening crowds, then stroll across the Seine to Square René Viviani. Located in the 5eme on Quai de Montebello, it sits directly in front of Église St. Julian de Pauvre, possibly the oldest church in Paris. In the center is this tall triangular bronze fountain by Georges Jeanclos. The oldest tree in Paris is said to be here. May I just add that "the oldest" anything in Paris seems to always be open for discussion! I'm only reporting what I found on this site. I welcome differing opinions, so have your say!
When I visited in July, everyone was sitting and enjoying the view, reading, eating lunch, poring over their maps of Paris, and some were even lying in the grass for a little siesta. I took the photo below to illustrate the lovely flower beds and then realized that the couple in the background proves that Paris is indeed the City of Love!