No time for that, perhaps another time. This is the first time I'm going out of country so I'm devoting every second to Paris.
Definitely do notre dame, and then hit the latin quarter.
In a day just by walking, you can hit Notre dame, walk over to the latin quarter (Saint michaels fountain area on your map, just to the southeast) and it is a great place to shop and eat and rest.
Then head over to the Cluny museum- medieval art in a really neat old gothic mansion built in the same vein as Notre dame itself.
Beyond that, taking the Metro to Gare de Lyon and walking back up to the bastille is pretty damn cool.
...As far as the catacombs, the cemetary where Jim Morrison was buried is right by one of the most popular stretches of the catacombs- worth a trip- it is loaded with names you would recognize.
Also, when in the catacombs, pay attention to the access points of the french resistance that terrorized the nazis- they used the catacombs to creep around and strike all over the city.
You can see world war 2 scars everywhere- Look around the upper windows of old buildings- you will see chips and bullet holes where snipers would pop their heads out, tak a shot, and duck back for cover... most buildings still bear the scars.
It is really easy to walk past a place without realizing what happened there in history- there are so many layers, you could miss an entire century of cool shit without ever noticing.