It does not matter whether the french authorities checked only the green cards.
Since the couple admits the mistake of not carrying appropriate travel documents, they have to face the consequences. The immigration officer was well within their powers to deport people who do not have a visa.
Let us not play the racism card to our advantage when it suits us. Why did the couple not accuse the french authorities of not checking their Children's Visa to India? They seem to suggest that whatever the french did, the indians too should do.
It would be a good lesson to these careless people. Because of their tardy attitude their Children suffered.