Cani, I am definitely interested in the route you took.
I think there is a metro stop near the Jardins du Luxembourg so you could start there.
-Jardins du Luxembourg -- lovely to walk around, to just sit, can see the Palais du Luxembourg here. If you want to see the Pantheon, it is just a short walk up a street from here, if not then...
-Walk down Boulevard St-Michel
-On the right you will see the Sorbonne University -- it is open to the public, so you can walk in if you have an interest and look around.
-Keep walking down Blvd. St-Michel and at the end you will be at the Seine River
-You will see Notre Dame off to your right, so you can walk over there and look inside -- gorgegous windows and impressive exterior. There is also a quaint little park behind Notre Dame if you want to take a little rest.
-Walk along the seine -- enjoy the cute little stands selling old books, drawings and various other things.
-You will see Pont des Arts -- a beautiful bridge. If you haven't already crossed the Seine, you could cross here.
-You'll see the Louvre as you go across.
-I forget how to get into the courtyard of the Louvre -- I'm sure a guide book can help you.
-Once inside the courtyard of the Louvre (a massive bldg -- the exterior blows me away every time I've been there -- you could spend so much time just enjoying it), you will see the glass pyramids that leads to the vistor center if you are going inside.
-With your back to the pyramids, walk through the Place du Carrousel
-Then through the Jardin des Tuileries. If you've ever seen the little sailboats being push in little ponds -- this is where that happens -- adorable. If you want to walk to the Terrace, you will be able to see the top of the Musee d'Orsay (IMO definitely want to make a stop here on another day)
-Continue walking and near the end you will see L'Orangerie on your left and Jeu de Paume on the right.
-Continue walking straight to the Place de Le Concorde -- you will definitely want to find a safe way to cross -- this is the dicey traffic circle I mentioned.
-Off to your right you will see Madeleine (modeled after a greek temple)and can make a detour to see it if you wish.
-At the other side of the Place de le Concorde, you are at the base of the Champs-Elysees. You will see the Petit Palais and then the Grand Palais on your left.
-The Champs Elysees is massive and pretty. This is where the Tour de France always ends.
-Walk straight along the Champs-Elysees to the Arc de Triomphe at the top. If you want to go to the top of it, you can see many sights in the city.
-I'd walk back down the Champs-Elysees until you get to Avenue Montaigne (so you may want to walk up one side of the Champs-Elysees and down the other side) on your right -- this is a large avenue -- you won't miss it.
-Walk up Avenue Montaigne (a street filled with very expensive designer shops) until the top.
-Near the top, on your right, when you get to Bldg. 3, look all the way to the top to the tiny windows, and wave to the little room I lived in for a short while.
-On your left, you will see a tunnel where cars are entering. This is the tunnel where Princess Diana was killed. At the top of the tunnel you will see, and can walk to, the original flame from the statue of liberty which was returned to France (If I recall correctly.) This is where many leave flowers and notes in memory of Princess Diana.
-I forget the specifics of this bit, but you can walk along the Seine River to the Champ de Mars, where you will see the Eiffel Tower.
This is a nice long walk -- would take
several hours. If you go into all the places I mentioned, and stop to really take things in, you wouldn't be able to get through it in one day -- but then break it up over however many days you like. A guidebook can give you a better sense of what you can fit in in a day -- this is truly a walk. Also, since I was pretty familiar with the city at this point, I was walking at a nice pace - if you are unsure of where you are at times, this changes the pace. But, it is definitely do-able to walk it within a day. Hopefully it gives you the sense that there is a lot to see walking around. When you check out at map, it really isn't that bad walking places -- unless you want to cram a lot in, then taking the metro makes sense.
Hope this helps -- have a blast!