Lily has lived in France for 10 years; Jack for five. They work as cleaners and baby-sitters, sending much of the money they earn to the other side of the world.
They are Filipinos, part of a large, mostly illegal, community in Paris.
Their son, Christopher, does officially exist. He was born in a state hospital and goes to a state nursery school. No questions have ever been asked.
At school, Christopher speaks fluent, three-year-old's French. At home, he speaks, Tagalog, the principal Filipino language.
In the past three months, Jack and Lily have emerged cautiously from the twilight zone. As a consequence, they - and thousands like them - have been caught in the full, confusing glare of French electoral politics.
Nicolas Sarkozy, the Interior Minister, wants to become president next year. More than that, he expects to become president.
Earlier this year, to appeal to right-wing voters, he drafted tough new laws to control immigration and remove illegal residents.
In June, to appeal to centrist voters, he sent a circular to government officials, softening the new law. Any illegal immigrant who had a child in a French school, and had integrated into French society, could apply for legal residence and work permits.
M. Sarkozy expected a couple of thousand people to apply. Town halls around the country were besieged. Some of the people in the queues were from the much-talked-about illegal immigrant communities in France - the Africans and the north Africans. Many more were from the never-talked-about, invisible, immigrant communities, principally the Chinese but also the Filipinos.
M. Sarkozy, taking fright, turned hard cop again. He is reported to have issued orders that town halls and prefectures (national government offices) should find technicalities on which to reject as many applications as possible.
Of 30,000 applications, only 6,924 were accepted. There was no logic to the successes and failures but there was a pattern. Those applications processed well before M. Sarkozy took fright had a much better success rate than those made later.
Jack and Lily are a perfect case in point.
Lily's brother applied early. He has been living in Paris for five years. His child, although born in France, lives in the Philippines. He was accepted.
Jack and Lily applied rather late. They used a French lawyer who insisted on preparing fussy dossiers, charged a lot of money and proved to be largely incompetent. They matched almost perfectly the original Sarkozy profile of immigrants with a "French" child.
They were rejected. They were told that they had failed to provide all the documents needed under a long-standing amnesty for immigrants who have been present in France for 10 years. In other words, they were rejected under the rules of a scheme for which they had not applied.
Like all the others who came forward but were not chosen, Jack and Lily are now in an even more bizarre, twilight world.
The state has their names and address. It knows that they are working in France, using French schools and health services, without paying taxes.
Logically, they should be arrested and thrown out of the country. The state has said that it has no plans to do so. In short, Jack and Lily - and all the other Jacks and Lilys - have been told to go back to being illegal.
However, Lily has uncovered an interesting fact. One of the employers of her formerly illegal brother is a lawyer who is a close friend and adviser to M. Sarkozy.
Lily has been to see the lawyer. She has explained the unfairness of the situation. The lawyer has agreed to see what she can do.
In other words, Lily is trying to use personal connections to circumvent the rules. The French call this "Systeme D". The "d" stands for débrouiller - to muddle through.
Lily should be given her papers without any further delay. What other proof does M. Sarkozy need that she is fully integrated in French life?
Amol Rajan
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