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The train was travelling between the Normandy cities of Rouen and Caen, Transport Minister Philippe Tabarot said on X.
The train derailed at around 7:45pm local time (1745 GMT), according to local authorities, who activated a mass-casualty response plan. Some 130 firefighters, five medical teams and 80 vehicles were deployed to the scene.
One passenger, 24-year-old Louis, described the moments before the derailment to ICI Normandie radio, saying there were several jolts before the movement grew increasingly violent.
He said he was unable to remain in his seat as windows were partially shattered and stones from the track entered the carriage.
Rouen prosecutor Sebastien Gallois said 44 people were injured, including the 18-year-old woman, who was evacuated in critical condition.
Tests for drugs and alcohol carried out on the train driver returned negative results, Gallois said.
SNCF Reseau, which manages France’s rail network, said traffic on the line had been suspended and power to the tracks cut to allow emergency services to operate safely.
“The priority is to care for the passengers, then to restore safe operating conditions,” SNCF Reseau said.
Rail authorities and the police have launched an investigation into the cause of the accident.