The Mosquée de Paris, next to the Natural History Museum.
Not just a place for Muslim prayer, Mosquée de Paris also hosts a pleasant little café and a hammam where you can steam off Paris' dirt, get a massage and have various beauty treatments such as depilation.
Pantheon's Foucault's Pendulum. Driven by the Earth's rotation the constantly swinging pendulum has roughly told the time since 1851. More Pantheon.
A couple of blocks after the Mosque squats the entertaining Pantheon, followed immediately by the Luxembourg Gardens, a gorgeous, colourful space, with shade and plenty of free seating if needed.
Luxembourg Gardens. Much appreciated lunch-time shade in the summer, when the sun chooses to shine.
Or leg-browning on free chairs with plenty of impressionist colour.
A typical Frenchman having a wild time with two mistresses (and a horse?!). Next, Marais Quarter.