The P28 plane had taken off from Wellesbourne in Britain on Saturday for the French seaside resort of Le Touquet, the maritime prefecture said.
The British-registered plane had taken off with five other light aircraft as part of a joint outing, the prefecture said.
Its last known position was half-way over the Channel some 25 miles (45 kilometres) from Dungeness in the south east of England, according to the UK coastguard.
A substantial search operation by both the French and the British authorities on Saturday proved fruitless.
A spokesman for the French emergency services said, “It crashed into British waters for an unknown reason,” according to French news reports.
“British Coastguard launched an operation supported by French aircraft and boats including the Abeille-Languedoc (Languedoc Bee) tug, which has been chartered by the French Navy,” the spokesman added.
The search resumed on Sunday with a French helicopter and a French navy rescue boat, as well as a UK coastguard plane.
A number of commercial ships in the area had also been asked to help, but no debris has yet been found and no witnesses reported seeing the plane go down, the prefecture told AFP.
Britain’s Sunday Telegraph newspaper reported that the single-engine plane was owned by a staff instructor at a flying school based in Wellesbourne.
It named him as Guy Wakeley. The flying school’s website lists his former roles as chief executive for Morrison, a social housing maintenance group, and financial services group Equiniti.
The website said it was holding a “Club Fly-Out” to Le Touquet on Saturday.
An official at the school declined to comment on who was aboard the plane to The Sunday Telegraph.