In addition to best film, Amour took best director and best script for Austrian Haneke and its French stars Jean-Louis Trintignant and 85-year-old Emmanuelle Riva picked up best actor and actress.
The drama won the Palme d'Or at Cannes last year and a Golden Globe for best foreign language film in January. It has five nominations in Sunday's Oscars including best actress and best film.
A two-time Oscar winner for the 1990 hit Dances with Wolves, Costner, 58, meanwhile, was visibly moved by the standing ovation he received as he accepted his honorary Cesar.
As well as Dances with Wolves for which he won best picture and best director Oscars, Costner has starred in a string of box office successes including Field of Dreams, "The Untouchables" and The Bodyguard with the late Whitney Houston.
"I love the process that goes into making films... they remind us of what it means to be a hero, that heroes don't always win," he told a star-studded audience at the ceremony in Paris.
Best foreign film went to Ben Affleck's Argo. Affleck, who directed and starred in the film, was not at the ceremony.
Since it beat 21 other movies to claim the top prize at Cannes, Haneke's French language Amour has gone from strength to strength.
Haneke, 70, has established himself in recent years as one of the most important film directors in Europe. His films include The Piano Teacher, Cache and Funny Games.
Amour had been in competition at the Cesars with Noemie Lvovsky's Camille Rewinds (Camille Redouble) about a woman who travels back in time to relive her 1980s schooldays.
Camille, the surprise hit of 2012 began with 13 nominations compared to 10 for Amour but finished the evening empty-handed.
Despite its difficult subject, Amour has been both a critical and box office success.
Over 680,000 people have been to see it in France, while the overseas audience figure stands at 1.7 million. It has been shown or is to be shown in some 50 countries worldwide.
On Sunday it will hope to pick up more accolades with nominations in the five categories of best actress, best director, best script, best film and best foreign language film.
Riva, who celebrates her 86th birthday on the same day, has already made history by becoming the oldest woman to be nominated in the best actress category.
Other contenders at Friday's Cesars had included Benoit Jacquot's Farewell, My Queen (Les Adieux a la Reine), a fictional account of the last days of Marie Antoinette, with 10 nominations.
Jacques Audiard's Rust and Bone also had nine nominations including best actress for Marion Cotillard.
Other nominees in the best film category included the thriller In the House (Dans la Maison) in which Francois Ozon explores the perils of a teacher getting too close to one of his students; the comedy What's in a Name? (Prenom) by Matthieu Delaporte and Alexandre de la Patelliere about a group of 40-something friends' dinner party disaster; and Leos Carax's fantasy drama Holy Motors about a man living parallel lives.