The family pulled up to a gas station on the A29 in Normandy when they heard a noise coming from the box, France Bleu radio reported.
Upon opening it, they were shocked to find two people hiding inside.
Images posted online appear to show the moment the migrants were discovered in the roof box.
Officials said the 16-year-olds from Eritrea and Guinea had targeted the car because of its British license plates and hoped to reach the UK.
However, the British couple and their two children had just arrived in France and were heading to their holiday destination after discovering the migrants.
French media reported that the family asked a bystander to call the police as the migrants fled the scene.
The migrants were reportedly arrested by local police and have since been released.
British tourists told police they had arrived in France via the Eurotunnel and spent the night in Calais, where the migrants are said to have entered their luggage trunk.
The couple filed a theft complaint because luggage had been removed from the box.