The incident occurred at the police station in the second arrondissement of central Paris on Monday when a young couple was carrying out some administrative tasks.
Then, according to the man's Facebook post afterwards, his partner asked for permission to feed their 2-month-old child while they waited.
An attendant checked with her senior, only to return and say it was against the rules. This news was followed by a visit from a senior staff member, who "took a very hostile tone".
According to the husband the policeman said: "It's out of the question to nurse your child in public like this, you're not going to impose this on everyone."
The couple then left, but returned to get the name of the senior police officer, information which was reportedly refused to them.
The woman later wrote that she was called a bad mother by a separate officer, who "attempted to humiliate" her.
The couple later set up a petition in an attempt calling for France's interior minister and the police chief of the 2nd arrondissement "to denounce this act of misogyny and to public support breastfeeding in public and in police stations".
The petition has attracted 13,500 signatures in the three days since it was launched.
The mayor of the second arrondissement said he was "outraged" to learn of the altercation, suggesting it was an "attack on the freedom of women", reported 20 Minutes newspaper.
Public breastfeeding in France is legal, although breastfeeding isn't as popular among French womenas it is in northern European countries and the United States.
One study in 2014 found that French women are among the least likely to breastfeed in Europe.
French national health authorities says mothers should breastfeed for at least four months and note six months of breastfeeding is the best for the child’s health. According to the World Health Organization breast milk is the “perfect food” for newborns because it contains all the nutrients a child needs.