A police official said the teen had pledged loyalty to ISIS in a recent video.
The prosecutor's office said around 70 grams of TATP were seized in the Montpellier-area home of a 20-year-old man, along with a liter each of acetone, oxygenated water and sulfuric acid.
TATP, which can be made from readily available materials, was used in the deadly November 2015 attacks in Paris and the March 2016 attack in Brussels carried out by Islamic State extremists.
Two other men were arrested, a 33-year-old and a 26-year-old, along with the teenage girl, according to the prosecutor's office, which handles terrorism investigations in France.
The police official, speaking on condition of anonymity to discuss the investigation, said one of the suspects was believed to be planning a suicide attack but that the investigation had not yet uncovered a specific target.
He said person in the group had tried to reach Syria in 2015 and was known to intelligence services. The group—notably the girl—attracted new attention with their social media postings, he said.
Interior Minister Bruno Le Roux said the arrests in three locations in the Montpellier area "thwarted an imminent attack on French soil."
The country's prime minister praised the work of anti-terror investigators.
"Faced with the heightened threat, there has been an extremely strong mobilization of our intelligence services to ensure the French are protected to the utmost," said Prime Minister Bernard Cazeneuve.
In addition to France, a 44-year-old man was also arrested in Britain at Gatwick Airport on suspicion of planning a terror attack.
In a statement from British anti-terror forces, the man was arrested Thursday evening after landing in Britain on a flight from Iraq.
"The man was arrested on suspicion of planning a terror attack and taken to a police station in London," said the statement.