Here are just a few of my favorite authentic parisian addresses:
Spa Cinq Mondes skincare and body therapies inspired by ancient rituals from all over the world.
Septime excellent, snob free, modern rustic bistrot.
Bon Ton close to Merci, kids boutique, furniture, clothes, toys.
Sola out of this world sushi, seriously.
Jardins du Luxembourg by far, the most romantic parc in the city. Grab a book, wander around, great people watching, take a catnap, get into a heated conversation on existentialism, and then make out/up on a bench.
Fromagerie QuatreHomme (voted best cheese merchant of Paris) in Saint Germain des Pres, Rue de Sèvre. And a door down, an authentic boulangerie (bakery), and an other door down, an épicerie (fresh veggies). Get a glorious pique-nique to go.
Bâteau Mouches tour the city from the perspective of drifting along the Seine river: spectacular sights of the most stunning highlights of Paris, and very romantic. Ideal also when your high heels gave up on you.
Solar Hotel cheap and clean, convenient central location. Or reserve a pied-à-terre with Air BnB in vibrant neighborhoods: Saint Germain (-Des-Prés), Le Marais.
Vélib rent a bicycle anywhere in the city, you'll need a credit card, and the first 30min are free, so basically, grab a bicyclette, ride it to wherever, within half an hour, tke a break, and hop back on. You'll get around Paris for free, and get these decadent buttery 'breakfeasts' burnt out in no time.