The aircraft was flying from the city of Rodez in the southern French department of Aveyron, the Figaro newspaper reported.
"More fear than harm," Cayeux said on Twitter.
She also thanked the firefighters and airport staff for their work.
A screenshot of a photo posted by French Minister Delegate for Territorial Entities Caroline Cayeux after a passenger plane she was travelling on rolled off the runway while landing at Paris Orly Airport. October 20, 2022.
© Photo : Caroline Cayeux
Fly Amelia air company said that the incident occurred due to bad weather conditions.