The father was taken into police custody in the town of Dieppe, northern France as police continue investigate the circumstances around the baby's death, which occurred on one of the warmest days of the year so far.
According to initial reports in the French press, the father, who works at an engineering firm based near the city of Rennes, western France, took his wife to work at around 2pm on Thursday.
After dropping her off he was then supposed to take his son to nursery but apparently forgot and instead drove home to continue working, the website Normandie Actu reported.
At around 6pm that evening his wife called to remind him to collect the child.
He left and drove back to the creche. But when he arrived he was told his baby was not on the premises. It was then that two bystanders noticed the baby was in the back seat of the car.
Paramedics were immediately called but they could not revive the child.
The prosecutor of Dieppe, Valerie Cadignan told reporters that “the father had made a round trip without realizing the child was strapped in in the back of the car.”
After the father was taken into custody he reportedly told police he was suffering “fatigue and being overworked”.
A forensic examination of the child's body is to be carried out as well as a psychological examination of the father.
A similar baby-death occurred in Sweden in May 2013 when a father forgot to drop his baby off at nursery and instead went to work.
He only realized eight hours later.