While it is obvious the death of Jennifer needs to remain a secret, as one police officer needs to stake out the burial location at night (which he does not like to do), her death is widely announced throughout the village.
On the child's grave, Nathan, it says born 1988- passed away 1988. But during Thierry Rouget's questioning later in the episode, we learned that the baby died on an April 4th 1988 at the age of 11 months. Meaning he had to be born in May 1987, and not 1988.