"I am reaching out to Emmanuel Macron, and to his wife Brigitte Trogneux," she wrote.
"As a resident of France, my adopted home, I would like to meet with you and discuss Julian's situation. I am opening a new vegan restaurant in France in July, and I would like to extend my invitation to the new President and his First Lady.
"Join me on the day I open the doors, and we will sit and eat good food and discuss what can be done for Julian. France could display its strength, and so could you, if you give Julian asylum."
Anderson is partnering with chef Christophe Leroy for her new restaurant, which is named Le Table du Marche.
The new establishment is said to open its doors on July 4 for just 50 nights.