I don't know about the first major film who used drones to film scenes that in other films were done with helicopters.
But I found this list which has 7 major movies that used drones, and a couple of those are James Bond movies which you quoted in your question.
Sam Mendes’ Skyfall, starring Daniel Craig, Javier Bardem, and Naomie Harris, was the first of the James Bond movies to use drones for filming aerial footage.
The opening scene was shot using drones. With a moving train, a low-flying helicopter dropping and collecting people from the train, bullets flying, explosions and soldier action, it was not an easy scene to capture on camera.
- The Wolf of Wall Street (2013)
Martin Scorsese’s film The Wolf of Wall Street used the US-based drone cinematography company Freefly Cinema to capture the aerial shots of the pool party.
In Chappie, the latest movie by South African director Neill Blomkamp after the critically acclaimed District 9, drones have been used intensively.
The camera on the drone was used as the POV (Point of View) of one of the robot characters.
Sam Mendes’s Spectre, James Bond‘s latest movie, makes ample use of drone shots.
Helicopter Film Services (HFS), a UK-based helicopter and drone aerial filming company founded by Jeremy Braben, was the company chosen to provide drone aerial footage.
Team 5 Aerial System Rentals are another experienced California-based aerial company who have embraced drones as a way to get unique aerial shots from a lower perspective than a helicopter.
- Captain America: Civil War (2016)
Due for release in 2016, Captain America: Civil War features drone footage from Pictorvision and aerial filming from Helicopter Film Services (HFS).
More details can be found HERE.
Another movies scenes filmed with drones HERE.