Herzog reached the Himalayan peak's summit without oxygen in 1950 alongside his compatriot Louis Lachenal,.
He lost several fingers and toes to frostbite on the way.
The feat brought him huge notoriety around the world.
Herzog wrote best-sellers on climbing. His book Annapurna sold 12 million copies and was translated into 40 languages.
Herzog was the national hero France so needed to help lift its spirits in the grim post-war years.
He went on to become an MP and mayor of Chamonix, the skiing and mountain-climbing centre in the French Alps, and, in 1963, youth and sports minister under the presidency of General Charles De Gaulle.
He also ran several companies, including the one that runs the Mont Blanc tunnel.
But that image has been tarnished recently by accusations that he had embellished his role in the Annapurna ascent.
This year his daughter published a work of fiction in which she portrays him as a serial adulterer who neglected his children.
The book even suggests Herzog and Lachenal may never have actually got to the top of Annapurna.
Herzog lived his later years in the Paris suburb of Neuilly but will be buried in Chamonix.