Officials said Cantat was asleep at the Bordeaux, southwest France home of Kristina Rady, 41, when she hanged herself on Sunday.
The couple's two children, a 12-year-old boy and seven-year-old girl, were not present at the house when Rady committed suicide, but one of them made the discovery when returning home around midday Sunday, officials said.
The 45-year-old frontman for the band Noir Desir has been questioned by police in Bordeaux but no action has been taken against him.
"According to initial findings confirmed by some technical data, the death was due to suicide by hanging," said a source close to the investigation.
Known for his edgy music and dark lyrics, Cantat married Rady, of Hungarian origin, in 1997, but they separated soon after their daughter's birth when he met Trintignant.
Rady was a writer and theatre actress who had translated works into Hungarian, including Marjane Satrapi's award-winning animated work film Persepolis.
She had spoken out in defence of her ex-husband during his trial in Lithuania, saying he had never been violent with her during their marriage.
This is so sad. :-( Her poor children. :-((