According to Reuters, the bodies of 5 people, including a young girl, were found at the Wimereux beach in northern France.
The incident happened after around 112 passengers being transported on a small boat began to panic, and several people fell into the water.
Around 49 other migrants were rescued, but around 58 decided to stay on board and try to finish the trip to the UK.
Prefect Jacques Billant stated to reporters: "A tragedy occurred on a boat overloaded with migrants early this morning. We deplore the deaths of five people, a seven-year-old girl, a woman and three men.
"The engine stopped a few hundred meters away from the shore and several people fell into the water."
"They did not want to be rescued, they managed to restart the engine and headed towards Britain."
Over 7,500 migrants have arrived in the UK this year alone, and tens of thousands since 2018. They usually travel the channel from France in small, unreliable dinghies and the boats are usually overcrowded.