Philippe Graffart, 42, was sentenced on a reduced charge of culpable homicide instead of murder, after psychiatric findings showed he had "diminished responsibility" for suffocating his son Keryan with a pillow in their apartment.
Murder is punishable by hanging in Singapore.
Judicial Commissioner Hoo Sheau Peng said she took into consideration the grievous nature of the offence, the fact that it had been committed against a vulnerable child, and the fact that the offender was the child's own parent.
For culpable homicide without the intention of causing death, Graffart could have been jailed up to 10 years, caned and fined -- or any combination of the three penalties.
Graffart looked impassive when his sentence was read out, staring straight ahead at the judge.
Representatives from the French and Belgian embassies were present during the High Court hearing, as well as two of Graffart's former colleagues who briefly spoke to him before he was taken away to serve his sentence.
His Singaporean lawyer Ramesh Tiwary told AFP after the session that Keryan's death is something Graffart "will have to live with for the rest of his life."
After the killing he unsuccessfully tried to commit suicide by crashing his car before giving himself up to police.
The family had moved to Singapore from Luxembourg in September 2013 after Graffart, a financial executive, was transferred by his employer, European firm Nordea Investment Management.
Their marriage broke down early the following year.
At about lunchtime on October 5, 2015, Graffart was told about a development in his custody suit which left him distraught, court documents said.
When the boy was asleep, Graffart placed a cushion over his son's head until he stopped moving.
After kissing his son goodbye, Graffart went on a drive and crashed his car on purpose on a highway after unbuckling his seatbelt. But the safety airbags saved his life.
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