The body of the victim was discovered around 2 am this Friday, at his home, in the Part-Dieu sector of the 3rd arrondissement of Lyon (Rhône).
The 30-year-old is believed to have died after being beaten with a hammer, local media report.
Her spouse, the main suspect, is actively sought by investigators from the Departmental Security, in charge of the investigations.
The prosecution opened an investigation for "intentional homicide".
In 2020, 90 women were killed by their spouses or ex-spouses.
In 2019, 146 feminicides were recorded by the government.