Marchal, a senior researcher at the Paris Institute of Political Studies (Sciences Po), is due to arrive in France later Saturday, according to the president's office.
In a statement late last week Emmanuel Macron, the French president had said he was "pleased" by the release of Mr Machal and urged Tehran to release Ms Adelkah who remains in custody.
Iran and France swapped an Iranian engineer who had been arrested over alleged violation of the U.S. sanctions and a French national imprisoned in Iran for acting against national security.
Iranian media earlier reported about the decision of Paris and Tehran to exchange prisoners.
The Trump administration on Sunday harshly criticized France for releasing an Iranian man wanted for prosecution by the United States in an apparent prisoner swap with Iran.
There engineer was threatened with charges of attempted illegal imports of American military technology in the interests of one of the Iranian companies. Iranian state television later said he was already on a flight back to Iran's capital, Tehran.
A spokesman for the Iranian judiciary hailed the exchange as "an act of mutual cooperation".
In Paris, their support committee has always claimed their innocence and demanded their immediate release, fearing for their lives. Iran said Saturday that 123 more people had died from coronavirus, raising the country's official death toll to 1,556.
Ahead of Iran's celebration of the Persian new year starting on Friday, authorities have released a number of global prisoners.
British-Iranian aid worker Nazanin Zaghari-Ratcliffe, held since was among those who received furlough.
Iran is still holding U.S. citizens Siamak Namazi - who was convicted for charges including espionage and collaboration with the United States government - his father Baquer and environmental expert Morad Tahbaz.