A French only document will cause hardship if one wants to enter the neighboring country of the United States with their child.

It can cause hardship for the child later on life when they need to show their official birth certificate in other countries.

This may affect you if you want to cross the border with your child with only a birth certificate. 

It may affect your child if they get married here and then want to move to another country.

It may affect your grandchildren if they want to apply for US citizenship via their grandparents.
etc. etc.