The New Zealanders needed to win by two goals to have any hope of advancing at the Paris Games.
The tournament's top scorer, Marie-Antoinette Katoto, scored both of the host nation's goals, while Kate Taylor scored from long-range for the Ferns just before halftime this morning (NZ time).
The Kiwis finished bottom of Group A, while France are top and into the quarterfinals.
Football Ferns' coach Michael Mayne told Sky Sport that while they are disappointed they know "effort alone is not enough at this level".
The side lost 2-1 to the eighth-ranked Canadians in their first match in the wake of a huge scandal surrounding the Canadians using a drone to spy on the Ferns during their training.
New Zealand were beaten 2-0 by Colombia in their second Games group on Monday.
Defending champions Canada reached the quarter-finals on Wednesday, thanks to a 1-0 win over Colombia in Nice.
Colombia also booked their spot in the knockouts on Wednesday, along with France, Germany, Japan and Brazil, but Australia missed out.
Canada appeal dismissed
Canada's appeal against their points deduction at the Olympics amid a drone scandal has been dismissed by the Court of Arbitration for Sport, CAS said on Wednesday.
Canada were docked six points, while coach Bev Priestman, a former head of Football New Zealand, and officials Joseph Lombardi and Jasmine Mander were banned from any football-related activity for one year by FIFA after New Zealand complained that Canadian staff flew drones over their training sessions before their opening match.
"The application filed by the Canadian Olympic Committee and Canada Soccer in relation to the six-point deduction imposed on the Canadian women’s soccer team for the football tournament at the Olympic Games Paris 2024 has been dismissed," CAS said, with the reasoned decision to be published at a later date.
"The Applicants sought a decision from the CAS Ad hoc Division either cancelling or reducing the points deduction imposed by the FIFA Appeal Committee in its decision of 27 July 2024 after it established that breaches of the FIFA regulations applicable to the Olympic football tournament concerning the prohibition on flying drones over training sites had occurred."
Canada Soccer said it was disappointed with the decision, and continues "to believe that our players should not have been unnecessarily punished for actions that were not their own."
The national federation added that an independent external review had begun that would initially focus on the incident at the Olympics before looking at other issues, amid media reports that drone use may have predated the Paris Games.
A joint statement from Canada Soccer president Peter Augruso and chief executive and general secretary Kevin Blue said that Sonia Regenbogen would lead the review, describing her as a "leading Canadian expert in conducting independent workplace investigations".
On Monday, Sport Canada said it was withholding funding allocated for the salaries of Priestman and the two other suspended team officials, calling the drone scandal that has rocked the Paris Olympic tournament an embarrassment to all Canadians.
- RNZ and Reuters
