“President Jacques Chirac died this morning surrounded by his family, peacefully,” his son-in-law told AFP.
Mr Chirac served two terms as French president and took his country into the single European currency.
The French National Assembly has observed a minute’s silence in homage to him.
The president of the European Commission and former Luxembourg premier Jean-Claude Juncker has said he was “moved and devastated” to learn the news.
“Europe is not only losing a great statesman, but the president is losing a great friend,” his spokeswoman quoted Mr Juncker as saying.
One of Mr Chirac’s major political reforms was to cut the presidential term of office from seven to five years.
He was seen as the focus of opposition to the US-led invasion of Iraq in 2003.
He served as head of state from 1995 to 2007, with his health steadily deteriorating since then.