Veil, a women's rights icon who served as the first president of the European Parliament, died at her home, her son Jean Veil said.
Expressing his condolences, French President Emmanuel Macron tweeted: "May her example inspire our fellow citizens, as the best of what France can achieve."
Macron's predecessor Francois Hollande said she "embodied dignity, courage and moral rectitude."
"France has lost a figure the likes of which history produces few," French Prime Minister Edouard Philippe tweeted.
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Her standout achievement as a politician was shepherding a 1974 abortion law through parliament after a 25-hour debate during which she endured a torrent of abuse, with some lawmakers likening terminations to the Holocaust.
"I never imagined the hatred that I would unleash," the former health minister said later.
"There was such hypocrisy," she said. "The assembly was mainly filled with men, some of whom were secretly looking for contacts to arrange an abortion for mistress or a member of their family."
Her father, mother and brother died in the Nazi death camps. She and her two sisters, one of whom later died in a car crash, survived.
After the war she studied law and married Antoine Veil, who died in April 2013. The couple had three sons.
As a young judge she lobbied for improved conditions in French prisons before later throwing herself into the battle to end backstreet abortions.
A staunch believer in European integration, she became the first president of the European Parliament in 1979, a post she held for three years.
Polls consistently showed her to be one of France's most popular and trusted figures.