There's a particular Paris weather, usually in February or November, where it rains for six days straight and the sky never really gets light. The trick to dating through it is to pick venues that absorb time. A café you can sit in for three hours, a museum with enough rooms that you can pace yourself, a bookshop with seats. The places below all do this, and most of them are not on the standard tourist circuit.
Shakespeare and Company and the café next door
Shakespeare and Company on Rue de la Bûcherie is touristy and worth it anyway. The upstairs reading rooms have benches, an old piano, and beds where you can sit with a book for an hour without anyone telling you to leave. The shop is open until 10pm most nights, which is unusual for Paris, and the selection of English-language books is genuinely good.
The café next door, opened by the same family in 2015, does proper coffee and a decent lunch menu. A tartine and a coffee are around twelve euros. The combination of the two buildings is enough for a long rainy afternoon, and the views of Notre-Dame from the upstairs windows have come back into their own since the cathedral reopened.
The Centre Pompidou and the Marais after
The Pompidou is closing for a long renovation, but as of writing the permanent collection is still accessible and the building is one of the best places in Paris to spend a wet afternoon. The fifth floor has the historic modern collection, the fourth has contemporary, and the views from the escalators on the outside of the building are the best free panorama in the 4th.
After, walk five minutes to the upper Marais and have a drink at Café Charlot on Rue de Bretagne or, if you want something quieter, at Ob-La-Di on Rue Dupetit-Thouars. The 3rd absorbs rainy afternoons better than almost any other arrondissement because the streets are narrow and the cafés are warm.
The Hammam at the Mosquée de Paris
The hammam at the Grande Mosquée de Paris in the 5th is open to women most days and to men on Tuesdays and Sundays, which means it's not a couple's date in the strict sense. But you can meet at the tea room afterward, in the courtyard with the fig trees, and that's its own kind of date. Entry to the baths is around twenty-five euros, more with a gommage and massage.
The tea room is open to non-bathers too, and a mint tea and pastry costs around eight euros. The room is tiled, warm, and full of regulars reading newspapers. It's the closest thing Paris has to a Moroccan riad, which is to say not very close, but close enough on a wet Sunday.
The Musée de la Chasse et de la Nature
The Musée de la Chasse on Rue des Archives in the 3rd is the strangest museum in Paris and one of the best for a date. It's nominally about hunting, but it's really about the relationship between humans and animals across art history, and the curation is witty and odd. There's a room with a ceiling installation of owl heads, a unicorn cabinet, and a series of contemporary art pieces interleaved with 17th-century rifles.
Twelve euros entry, two hours easily, and you'll both have something to talk about for the rest of the evening. The Marais around it is full of cafés for after.
The Galerie Vivienne and Legrand Filles et Fils
The Galerie Vivienne, off Rue des Petits Champs in the 2nd, is the most beautiful of the covered passages and the least crowded after lunch. The mosaic floor is from 1823 and most of the shops are still independent. A Priori Thé does a long-standing afternoon tea, and Legrand Filles et Fils, which has been there since 1880, is a wine shop with a small bar where you can drink a glass of Sancerre standing up among barrels.
The whole experience is theatrical without trying to be. Two glasses of wine, a plate of cheese, and an hour of looking at things you can't afford in the surrounding shops adds up to something better than dinner.
The bouquinistes and the bookshops of the 6th
When the rain isn't too heavy, the bouquinistes along the Quai de la Tournelle and Quai de Montebello stay open under their green boxes. Browse for old maps and Tintin books and don't buy anything. When it gets heavier, retreat into the 6th: La Hune on Rue Saint-Benoît, the Gibert Joseph on Boulevard Saint-Michel, the secondhand bookshops on Rue Monsieur le Prince.
End at Café de la Mairie on Place Saint-Sulpice, which is where the writers actually go and which has held its prices in a neighborhood that hasn't. A coffee is three-fifty, a glass of wine is six. Sit by the window and watch the square.
Aquarium de Paris under the Trocadéro
The Aquarium de Paris is built into the hill under the Trocadéro gardens and almost nobody goes. Twenty-three euros entry is more than I'd usually recommend, but the place is enormous, mostly empty on weekday afternoons, and the dark rooms with the tanks are unexpectedly good for a date. There's a shark tunnel, a touch tank, and a small cinema room that plays nature films.
Afterward, the Trocadéro has covered arcades on the museum side that get you most of the way to a metro without going outside, and the Café de l'Homme inside the Musée de l'Homme has a terrace under glass facing the Eiffel Tower. The view alone is worth the coffee.