The man, whose name was not released, was found dead at Tarbes in the Pyrenees. He had been hospitalised following his arrest on suspicion of murder
on Sunday evening but was not under police surveillance and was able to escape from the clinic 24 hours later.
"The first findings of the investigation indicate that the baby was strangled by his father," said prosecutor François Jardin, adding that the man
had left a suicide note to that effect.
The father had taken the baby from the home of his mother on Friday afternoon after a family judge ordered her to grant her estranged partner
access to his son.
The baby's body was discovered on Sunday morning in a hotel room on the outskirts of Tarbes.
Last week, a two-year-old toddler drowned at Lespinasse, also in southwestern France, after being driven into a canal by the suicidal 52-year-old girlfriend of her father. The girlfriend also died.
At the start of month, an eight-month-old baby died in the Gard region of southern France after allegedly being repeatedly thrown on the floor by his
21-year-old student father following a row with the estranged mother.