I’m trying to understand if Fight Club by Palahniuk would fit into the neo-noir genre. I’m thinking it would, because it has some of the elements: the troubled protagonist (narrator/Tyler), the femme fatale (Marla Singer), crime and danger (Fight Club and Project Mayhem activities). Would that be a correct assessment?

Chuck Palahniuk's Fight Club fits most neatly in the more general genre of satire, because it borrows from the conventions of contemporary life and other literary genres to point out ironies in them (for example, Fight Club's absurd addictions to and excesses of consumerism). As such, it is hard to place neatly into a genre. Still, Fight Club has many affinities with the neo-noir category, as well as its direct precedent, a genre known as film noir, which employed post–World-War-II innovations in narrative style and cinematography to explore themes that had previously been "too dark" for Hollywood. The "troubled protagonist" and "femme fatale" figures which you mentioned originated there.
Fight Club still fits best in the neo-noir category. The trope of white masculinity that it develops departs from film noir, focusing on an upper-middle-class protagonist (Tyler Durden) instead of a working-class one. Also, Marla Singer, his femme fatale, is cast more as a competing protagonist than a complementary figure or a persistent risk lurking in the background. Finally, while film noir movies are usually situated in the dark underground of an otherwise unassuming city, Fight Club's entire city is crumbling and infested with criminals.