"The French authorities in this difficult context have taken steps with Iranian authorities to get information from them on her situation and the conditions of her arrest and asked for consular access," Foreign Ministry Spokeswoman Agnes von der Muhll said in a statement.
"No satisfactory response has been given to these requests. France calls on the Iranian authorities to bring to light Mrs Adelkhah's situation and reiterates its requests, in particular the authorization of consular access without delay," she added.
Foreign-based Iranian media reported Adelkhah, an anthropologist, was arrested in Iran in June by the Revolutionary Guards for allegedly spying.
When asked earlier on Monday about the arrest, Iranian government spokesman Ali Rabiei was quoted as saying by the semi-official Tasnim news agency as saying that he had heard reports of the arrest, but had no further information.
Adelkhah, an anthropologist, is Senior Research Fellow at Sciences Po in Paris. Her arrest comes at a sensitive time when France is trying to de-escalate tension between longtime foes Iran and the United states over Tehran's 2015 nuclear deal.
Iran has previously arrested and charged French citizens in the past, including in 2005 and 2009.