Christophe Lalande, federal secretary of France's FNEC FP-FO education union, told Reuters earlier that he suspected that one of his staffers and her husband, missing on a holiday in Iran, were the two arrested.
While there was no "absolute certainty", there was a "strong presumption" that she has been arrested, Lalande said of his colleague, adding that she had been due back in France earlier this week.
The two arrested were accused of "organising chaos and social disorder aimed at destabilising (Iran)" in conjunction with foreign intelligence services, Iranian state TV on Wednesday cited Iran's intelligence ministry as saying.
The arrests coincided with a visit to Tehran by the European Union's Iran nuclear talks coordinator Enrique Mora, who held talks with his Iranian counterpart Ali Bagheri Kani, according to Iranian media.
Two other French nationals are held in Iran on national security charges their lawyers say are politically motivated.
Rights groups have accused Iran of trying to extract concessions from other countries through such arrests. Iran has repeatedly dismissed the charge.
Western powers have long demanded that Tehran free their citizens, who they say are political prisoners.
In January, an Iranian court sentenced French national Benjamin Briere to eight years in prison on spying charges, his Paris-based lawyer said, describing the trial as a politically motivated sham and his client as a "bargaining chip".
That same month, Iran re-imprisoned Franco-Iranian academic Fariba Adelkhah, sentenced to five years in jail in 2020 but recently living under house arrest.
France has warned Tehran in the past that the way it is handling the cases of its nationals held in Iran could sour ties.