The three victims, who included a 13-year-old, have been treated in hospital.
The adults were seriously wounded and taken to the Nice University Hospital (CHU), while the child, who suffered minor injuries, was admitted in a non-critical condition to the Lenval children's hospital in Nice.
On Wednesday, the man was no longer in a life-or-death situation, but the woman's condition had not yet stabilised, AFP reports.
The victims' identities have not been confirmed by Monaco authorities, but according to local reports, the attack targeted Vadym Yermolaiev, his partner and his son.
Yermolaiev, 58, is a wealthy real estate developer, who has been living in Monaco. He is a Cypriot citizen after renouncing his Ukrainian citizenship in 2019.
He has big interests in the wine and alcohol business in Russian-annexed Crimea, and since 2023 has been the subject of sanctions imposed by the government in Kyiv.
He was named the 39th richest Ukrainian by Forbes magazine in 2020, with a fortune of $230m (£173.8m).
