The teenager was detained in Quimper, western France, on Wednesday and later moved to Paris where she is being questioned in relation to the June disappearance of another 14-year-old girl from the Paris region.
Last week a 15-year-old and a 17-year-old were arrested for allegedly plotting terrorist activity in internet exchanges.
The younger of the two, who is believed to have been in touch with the missing 14-year-old on social networks, is suspected of planning to go to Syria and discussing terror attacks in France, sources told the AFP news agency.
The latest detainee is “suspected of wanting to leave to wage jihad, certainly in Syria, or possibly a terror attack”, Quimper deputy prosecutor Bérengère Prud’homme told AFP.
French security services estimate that more than 900 people have either left the country to fight in Syria, are on their way or hope to go.
Interior Minister Bernard Cazeneuve in April introduced a plan to combat the trend, including setting up a helpline for parents who believe their children are tempted to leave for Syria.
The government will propose a new anti-terror bill to parliament in September.
On Thursday President François Hollande ruled out working with President Bashar al-Assad's regime to fight the Islamic State fundamentalist group that has taken control of much of Syria and part of Iraq.