Cantat, 40-year-old lead singer of rock band Noir Desir, was found guilty of causing the death of Marie Trintignant.
He had told the court he slapped her several times during a jealous row; she died from head injuries a week later.
Ms Trintignant’s family believes Cantat’s sentence is too lenient and is asking for it to be increased.
The maximum sentence Cantat could receive from the court in Vilnius, Lithuania, is 15 years in prison.
The murder happened when the couple were staying at a
hotel in Vilnius last year, where Ms Trintignant was making a film
about the French literary heroine, Colette.
Cantat admitted having caused her death but said it was a tragic accident.