The child, who is believed to be aged 12 and from East Yorkshire, reportedly got into difficulty in a lake in Berny-Riviere in the north of the country.
After being found unconscious at around 6.30pm on Thursday, he was taken to hospital in Paris by helicopter but did not survive, according to local media.
A Foreign Office spokesman confirmed: "We are supporting the family of a British child who has died in France and are in contact with the French authorities."
The campsite, which is located in the Picardy region to the north-east of Paris, is understood to be managed by the European Camping Group and is popular with British holidaymakers.
Eurocamp is one of the tour operators which occupies a position on the site, although the boy and his family were not travelling with the company.
A spokeswoman for the firm said: "Eurocamp are profoundly saddened to learn of the tragic incident that occurred onsite at La Croix du Vieux Pont yesterday. Our thoughts are with the family at this very difficult time.
"We are actively cooperating with the campsite operator, the tour operator with whom the family are travelling, and with local authorities to determine the precise circumstances that led to the accident. A further update will follow."
European Camping Group said the boy and his family had been travelling with tour operator Venue Holidays.
A statement expressing "deep sorrow for the family" said: "The group and the camping direction and its staff, shocked by this tragedy, are with the holidaymakers and a psychological support was set up, 24 hours a day with an English-speaking French psychologist.
"The group, for the first time confronted with a fatal accident on one of its camping, collaborates with the authorities to shed light on the circumstances of the accident."
The campsite's website states it is spread over 100 acres with 660 camping plots and boasts a heated pool complex, as well as a lake surrounded by a man-made beach.