The French Coastguard said the aircraft is the "subject of a worrying disappearance" and a search for the plane was carried out "all afternoon" on Saturday.
The coastguard added that a Falcon 50 aircraft, a helicopter, and a tug boat that was already at sea were all used in the search operation, along with a British aircraft.
The plane was believed to be travelling in a group of aircraft heading to the same destination.
A spokesman for the French emergency services said: "It crashed into British waters for an unknown reason.
"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 adds.
Small planes such as the Piper PA-28 are typically equipped with lifejackets and life rafts in case of emergency.
Although the aircraft may have sunk, rescuers are continuing the desperate search for the pilot and passenger in the Channel.
All ships sailing in the area have been asked to search for any signs of the plane and report any sightings to French authorities.
The passenger and pilot of the plane have not yet been identified.