Two suspects - one a school employee - arrested in a probe into an alleged attack plot in France apparently travelled briefly to Syria, officials said.
Two others among the seven suspects arrested over the weekend have been freed, an official said.
On Monday, interior minister Bernard Cazeneuve said the arrests in Strasbourg, in eastern France, and Marseille, in the south, came at the end of a more than eight-month investigation that he said thwarted a "terrorist action envisaged for a long time on our soil".
A series of arrests in June and the arrests on Sunday put an end to the alleged plot, Mr Cazeneuve said.
The suspects are believed to have initially wanted to target the Euro 2016 football tournament earlier this year. After arrests were made at the start of the tournament in June, the focus is alleged to have changed.
Officials said investigators examining a telephone found with one of the Strasbourg suspects revealed numerous searches, including one of an amusement park, that could be of potential targets, adding that it was too early to speak with certainty.
Mr Cazeneuve has said investigators are studying whether the alleged attack planning was part of a larger plot to attack multiple sites simultaneously.
The interior minister, meanwhile, on Wednesday presented a decree to dissolve an association that provides aid to inmates and families, especially those convicted on terrorism charges, but that, he maintains, also encourages radicalisation and rallies those it oversees to the jihadi cause.
The move was among numerous steps, including closing radical mosques and expelling radical preachers, France is taking to try to draw down the terrorist threat.
France remains under a state of emergency imposed after deadly Islamic State attacks on Paris last year. President Francois Hollande has said he wants the extraordinary measures prolonged until presidential elections next spring, a move that requires parliamentary approval.
The officials said that two of the four suspects arrested in Strasbourg, Yassine B and Hicham M, both 38 years old and French, are likely to have travelled to Syria in 2015, going first to Cyprus as if on holiday, then making what is suspected to have been a quick trip to Syria.
The officials confirmed that Yassine B worked in a Strasbourg school. It was not immediately known if he was a teacher or had other contact with children.
Only one of the suspects in the Sunday arrests was known to authorities ahead of the sweep, a 26-year-old Moroccan arrested in Marseille.
He lived legally in Aveiro, in northern Portugal, and had been flagged to European authorities as someone working in a terrorist group. Portuguese police said they had been watching him since 2015. Of the three men initially arrested in Marseille, he is the only one still jailed.