During questioning, he revealed that he had hit the child because he could not stand the baby's cries and had shared the photo on Facebook "for fun".
A friend of the couple who saw the "abnormal" photo on the social networking site alerted the police.
The worried Facebook friend alerted police in Aisne in northern France, Le Parisien reported.
It prompted a police probe that led to both parents being charged with violence on a minor.
Police confirmed that the baby was indeed "in a bad state".
According to the investigators, the mother did not alert police because she was worried that her husband would leave her, the report added.