Aussant was born as Mathilde Céleste Gaudet in Donges, a commune in Loire-Atlantique department, on 27 February 1898 as the fifth of 11 children born to François Gaudet and Hélène Halgand. Her first job was working as a waitress before moving to Paris aged 25, after the death of her mother.
In Paris, Aussant worked in a chocolate factory, and later a school cleaner and caretaker of a block of flats. She married twice, both of her husbands being train drivers. Her first husband died in 1936, and in 1946, she married René Aussant, who later became an oyster farmer. She was widowed again in 1961. Her only daughter was born during her first marriage.
After she was widowed for the second time, Aussant moved in with her daughter in Paris. They relocated to Fréteval, Loir-et-Cher department in 1983. In 1999, aged 101, she moved into a retirement home in Vendôme, Loir-et-Cher department. Her daughter died in 2007. As a supercentenarian, she was reported to have lost her hearing.
Aussant died on 23 July 2011 at the age of 113 years, 146 days. At the time of her death, she was the 12th-oldest person ever to die in France.