Damn, a couple of months! I'm jealous.

Paris is one of the coolest cities to visit IMO, I fly over just to hang out 2-3 times a year.
Anyway...
Videogame stores and arcades, particularly retro stuff
On Bvd Voltaire between métro Place de la République and métro Oberkampf there are many game shops with a good selection of retro and Japanese imports. It's the closest thing like Akihabara outside of Japan.
Retrogame Shop on Rue Basfroi is also worth a visit.
Comic book/manga stores, especially bizarro/odd stuff (my French is lousy, but can muddle through Shintaro Kago books, by way of example)
A lot of Comic book stores are on Rue Dante and the intersection of Bvd Saint Germain and Rue Saint-Jacques.
Check out Un Regarde Moderne on Rue Gît-le-Cœur. Tiny bookshop stuffed to the brim with books of 19th century anatomical drawings, 60s drug culture, Japanese bondage art, punk zines, etc. etc. etc.
I've never actually bought anything there cuz it's almost impossible to move, let alone browse anything, but it's a sight to behold!
Museums and galleries that aren't super obvious, like Le Louvre ou Le Centre Pompidou, though I'll probably head there anyway
Halle Saint Pierre in Montmartre often has cool lowbrow art shows.
Concorde Gallery on Bvd Lefebvre shows lots of pinup/erotic art, also Musée de l'Erotisme in Pigalle has changing exhibitions. Au Bonheur du Jour on Rue Chabanais, small gallery for fin de siècle and early 20th century porn.
Musée des Arts Forains has lots of rusty old dilapidated fairground rides that could've been in a 90s music video. Musée de la Chasse (hunting museum) was recently redone in a very cool, tongue-in-cheek way.
Musée Fragonard, 19th century medical museum
Bit of a stretch, but vegan restaurants?
In France? Really!? Try some foie gras instead.
Any interesting places, like rock bars, tattoo parlours, good parks to get drunk in, and other adult pursuits…
La Féline, Rockabilly bar near métro Ménilmontant
La Musardine, erotic bookstore on Rue du Chemin Vert
Père-Lachaise, Montmartre and Montparnasse cemetaries are nice for a walk
The park around the Tour d'Eiffel is nice to drink at night and watch the lights show, but really any park is cool to chill