As a resident of Paris, I will suggest a path you can walk in one day.
Start at Denfert-Rochereau station, the Catacombes de Paris is off the eaten path. This is the official entry of Paris undergrounds. Lot of history, if you're not too scared to see skulls.
Then go north and follow Bd Saint Michel, you can stop at jardin du Luxembourg. Continue further north and once you reach Saint Michel station , you're at Quartier Latin. There is a café Malongo I like (50 Rue Saint-André des Arts, 75006 Paris)
On the Island Saint-Louis , there is a famous glacier Berthillon (good on summer). On the other island (Ile de la Cité) , there is church Notre Dame. The visit upstairs close at 14:00 but the Christian mass is open and free.
On the Seine right bank, the Louvre is on your left (West), you can enter at the museum by pont des arts or pont du carrousel. The photos of pyramid are stunning. You may need one full day to visit the Louvre.
Yes in one day, you covered the catacombs, Saint Michel, Notre Dame,Louvre