TRANSIT VISA: A transit visa is granted for the sole purpose of enabling the holder to travel through India to reach his/her ultimate destination. Change of purpose is not allowed. The visa will ordinarily be valid for a single/double journey and for entry within three months of date of issue. The Transit visa is valid for direct transit only for a maximum period of 3 days. Confirmed airline ticket for onward journey and valid visa for final destination are required. For a stay in India beyond 3 days, an appropriate visa should be obtained.
A transit visa cannot be given without proving the real intent of TRANSIT.
May be the kids were not qualified for transit visa and the frenchman was!!!! Who knows.