Virginie de Cellier pledged to support 35-year-old Constance Marten and her grandson, telling her: “You are not alone in this situation. We will support you as much as we can.”
Miss Marten and her partner Mark Gordon, 48, have been traveling around the UK by taxi since their car was found alight on the M61 in BoltonGreater Manchester, January 5.
Police believe the couple is sleeping in a blue tent and fear for the safety of the baby, who has not received any medical attention since his birth in early January.
In a letter sent to the PA news agency by a family representative, Mrs. de Cellier writes: “An open letter to my beloved daughter Constance.
“I know you well enough; you are focused, intelligent, passionate and complex, with so much to offer the world. So many of your friends have come forward to say such positive things about you, assuring us of their warmest love and support for you and your family.
“You have made a choice in your personal adult life that has proved difficult, however I respect it, I know you want to keep your precious newborn child at all costs.
“With all that you have been through, this child cannot be taken away from you, but instead needs to be cared for in a kind and warm environment.
“I want to help you and my grandson. You deserve the opportunity to build a new life, create a stable family, and enjoy the same freedoms that most of us have.
“Constance, I will do my best to stand by you and my grandson. You are not alone in this situation. We will support you in any way we can.
“I am willing to do whatever it takes to help you recover from this horrible experience so you can thrive and enjoy motherhood.
“I love you and miss you mom xx.”
It is the first time Miss Marten’s mother has spoken publicly about her daughter’s disappearance.
The missing couple has so far eluded the police, often moving around and covering their faces for CCTV footage.
A £10,000 reward is being offered for information leading to them being found safe.
Investigators said they had accumulated a significant amount of money in the months before their disappearance and used it to pay for hotels and taxis around the country.
The pair traveled from Bolton to Liverpool, then Harwich in Essex, then east London and then Newhaven in Sussex, where they were seen near the ferry port on January 8.
In an update on Sunday, the Metropolitan Police said they believe the family may be staying at a camp in Sussex.
Miss Marten, who comes from a wealthy aristocratic family, was a promising drama student when she first met Mr Gordon in 2016.
Since then, the couple have lived a reclusive life, and in September, when Miss Marten was pregnant, they began moving around rented apartments.
Gordon served 20 years in prison in the United States for rape and assault committed when he was 14.
Anyone with information can call the emergency room 020 7175 0785 or Crimestoppers anonymously at 0800 555 111.