"The four suspects were arrested after they bought acetone," a police source said, referring to a highly-explosive liquid that can be used to make bombs.
Other material that could have been used to make bombs, including oxygenated water and syringes, were found in the raid that led to the arrests.
Anti-terror police believe they have foiled a plot to launch an attack on French soil, although they do not know where or when it was supposed to take place.
The 16-year-old girl was reportedly spotted on social media saying she wanted to join armed Islamists fighting in Iraq and Syria or to carry out an attack in France.
The other suspects are 20, 26 and 33 years old.
Ban on jihadist website visits lifted
Facing a threat of terror attacks that is officially judged "very high", France has introduced a new anti-terror law but the Constitutional Council on Friday struck down one of its provisions.
The court found that a ban on "habitual" visits to websites deemed to incite terrorism was an infringement of fundamental freedoms.
Although the law exempted "good faith" visits, for example by journalists or researchers, plaintiffs argued that the wording was vague and left it to an individual to prove lack of criminal intention.