"President Chirac is being treated for a lung infection and I want to pay homage to the exceptional quality of the medical teams," Chirac's son-in-law Frederick Salat-Baroux told AFP.
Salat-Baroux, husband of Chirac's daughter Claude, then later Wednesday announced that his mother-in-law Bernadette, also 83, had also been admitted to the Pitie-Salpetriere hospital in Paris.
"Bernadette Chirac, profoundly affected by the death of her eldest daughter Laurence (in April) and exhausted for several days following the lung infection of her husband, was hospitalised on Tuesday," he said.
After the public announcement, Salat-Baroux again appealed for "tranquillity" for the couple and "respect for their private life."
Chirac has been hospitalised since Sunday and rumours that he had died were sparked early Wednesday when former housing minister Christine Boutin tweeted "Mort de #Chirac" (death of #Chirac).
She was widely criticised by the Chirac family and others for the false report.
She said in defending her tweet that she had "information that seemed to come from a reliable source. It's information that I believe the French are awaiting... you can see the buzz around this story," Boutin told AFP.
Chirac, who led France from 1995 to 2007, had just returned from a visit to Morocco with his wife when he was admitted to hospital in Paris.
The centre-right Chirac, who served two terms as head of state, is probably best remembered internationally for his opposition to the US military intervention in Iraq in 2003.
A small stroke while in office in 2005 weakened him, and he is now rarely seen in public.
In December 2015, he spent two weeks in hospital, suffering from what his family described as fatigue.
In recent weeks, his entourage said his health had improved.
Upon his hospitalisation, France's current President Francois Hollande spoke of the country's "support" for the former head of state "in the challenge he is going through."
Boutin, meanwhile, known for fanning controversy, is appealing a 2015 conviction for calling homosexuality an "abomination".