The driver was one of six given tickets for going at least 180 kmh on the A26, known as the "British Motorway", which links the port city of Calais with Reims.
The Voix du Nord newspaper, which first reported the racers, showed a picture of one of the stopped vehicles bearing logos for the Modball Rally, an annual event whose motto is "Drive all day... Party all night!"
Organisers did not immediately respond to requests for comment, but the Modball website says this year's rally began Sunday in London en route to Paris, the first leg of the rally.
The website says drivers are not supposed to race, but that doesn't stop dozens from competing to be the first to arrive at the daily destinations during the weeklong event.
Four of the drivers stopped Sunday were temporarily prohibited from driving in France, though the Voix du Nord said they were allowed to continue on their way after their teammates agreed to drive -- and they had paid a 750-euro (660-pound, $875) fine.
This year's Modball involves 180 modified speedsters heading from London to Paris, Lyon, Monaco, Venice and Vienna, where the rally is set to wrap up on Friday.
The race fee of nearly 3,000 pounds ($4,000) -- or 4,000 pounds for the luxury package -- also gives participants access to lavish parties, though the Modball website stipulates they are not "required to drink alcohol".
And the organisers insist they do not encourage speeding.
"We focus on the events each night and keep driving time down to ensure safe journeys between cities," they write on their Facebook page.