Pilots need extra training to land in adverse weather conditions.
Passengers on the 8.45am Flybe flight to Paris were just minutes away from landing at their destination when they were told they would have to go all the way back to Cardiff.
One passenger from Bristol missed a job interview in France because of the incident.
Cassandra Grant explained: "Twenty minutes outside Paris, the captain said, 'Unfortunately I'm not qualified to land the plane in Paris.
"'They are asking for a level two qualification and I only have a level five. We'll have to fly back.'"
The whole thing beggars belief. If I had not been on the plane, I would not have believed it.
Flybe passenger Cassandra Grant
A spokeswoman for the airline said Flybe backed the pilot's decision "100 per cent".
He had recently switched from flying a Bombardier Q300 to a Bombardier Q400 and has not completed the "requisite low-visibility training," she said.
The dense fog covering Charles de Gaulle airport had not been there when the flight took off, she added.
The plane was already three hours late due to bad weather in Wales.
The pilot's situation is "quite unusual but probably not unheard of," according to the Civil Aviation Authority.