The man was arrested in Paris on Monday, the prosecutor's in the western town of Niort said.
The discovery was made on Saturday when police in Niort visited the flat of a 27-year-old mother of three known to be a victim of domestic abuse and who had gone missing a week earlier, a police source said.
A "man with a bag" turned up at the same time, and officers found it contained "a woman's body parts", the source added.
The man, who was briefly detained then released, said he had been contacted by the victim's partner who had told him "to retrieve the bag and put it in the cellar".
Police found the woman's three children aged 18 months, four and seven years old alone inside the flat.
Regional newspaper Nouvelle Republique said the man had posted a video on TikTok on Monday, saying he had not killed the young woman along with two pictures of the happy couple.
On average, a woman is killed every three days in France.
On Friday last week, a 40-year-old man in the northern town of Compiegne confessed to having killed his partner, a 55-year-old trans woman, with an axe during an argument.
Some 94 women were killed by their partner or ex-partner in France last year, according to Justice Minister Eric Dupont-Moretti, after 118 such murders in 2022.
