Resnais, who was born in 1922 in northwestern France and started his career with mid-length films in the 1940s, rose to fame with "Night and Fog" and "Van Gogh", a short that won an Oscar in its category in 1950.
In 1959, with author Marguerite Duras as scriptwriter, he directed "Hiroshima, Mon Amour", a feature about a love affair between a French woman and a Japanese architect that secured his reputation as a feature-film director.
French President Francois Hollande joined a chorus of condolences for Resnais, described as a highly original and influential film-maker steeped in the pre-war cinema culture of the United States.
"He constantly broke codes, rules and trends while appealing to a vast audience," Hollande's office said in a statement.
The director won a lifetime achievement award at the Cannes Film Festival in 2009, while the Berlin Film Festival awarded him the Alfred Bauer prize for his last film, "Loving, Drinking and Eating", to be released in France this month.
One of his favourite actors, Pierre Arditi, hailed the director as extremely original.
"There is nothing that less resembles a Resnais film than another Resnais film," Arditi told BFM TV. "He always tried to avoid copying what he had done before, he didn't want to use any formula."
Thierry Fremaux, director of the Cannes Film Festival, hailed a director whose films have influenced generations of film-makers.
"He hit hard from the start with his short films in the 1950s and when the Nouvelle Vague arrived, he was sort of a big brother." (Reporting By Marine Pennetier and Nicholas Vinocur; Editing by Alistair Lyon)