To me the most beautiful part of Paris is along the River Seine. Both sides of the river are lined with pedestrian promenades, and over 30 bridges cross the river at various points around the City. One evening I took a leisurely walk from Quai Branly, pass Place de la Concorde to Notre Dame and the Pompidou Centre - which was around 5 km. The weather was great, and the buildings along the river were really beautiful in the bright yet soft sunlight.
I zigzagged along the river, crossing the bridges whenever I saw something interesting on the other side. You get the best views of The Louvre buildings from the South bank of the Seine.
I particularly like the area around Notre Dame where the river forks out around Ile de la Cite. Now you are not just looking at the two sides of the river banks, but also the island in the middle which makes things even more interesting.