The couple had been held by Iran since 2022 and sentenced by a court in October last year to 17 and 20 years in prison for allegedly spying for Israel.
France said the spying charges were unfounded.
They were released from the notorious Evin jail in November and had stayed since then at the French embassy.
Kohler, 41, and Paris, 72, survived an Israeli air strike on the Evin prison during the 12-day war in June 2025.
French Foreign Minister Jean-Noel Barrot said he had spoken to the couple.
"They shared with me their emotion and their joy to return soon to their country and their loved ones," he said in a social media post.
His ministry said Barrot had held discussions at the weekend with his Iranian counterpart Abbas Araqchi.
French MPs greeted the announcement of their release with a standing ovation at the National Assembly.
The pair are among dozens of foreign and dual citizens to be held in Iran in recent years, often on espionage-related charges.
Iran's official news agency IRNA confirmed the couple's release, saying it followed an understanding between the two countries and France would in turn release Mahdieh Esfandiari, an Iranian student living in the French city of Lyon.
Esfandiari was arrested last year over anti-Israel social media posts.
As part of the understanding, France would also withdraw a complaint against Iran in the International Court of Justice, IRNA reported.
The release of the French couple came as US President Donald Trump threatened that "a whole civilisation will die tonight" unless Iran reaches a last-minute deal with the United States to reopen the Strait of Hormuz.
Last Thursday a container ship belonging to French shipping group CMA CGM passed through the Strait of Hormuz, a sign that Iran may not consider France to be a hostile country.
with DPA
