Both companies said their decisions were made because the service was not profitable enough, Air France complaining of "poor commercial viablity".
But the flights have been scrapped after Trump pulled out of the 2015 nuclear deal and slapped sanctions on Iran, while also threatening sanctions against foreign companies that continued to do business with the Islamic Republic.
Netanyahu welcomes move
Israeli Prime Minister Benjamin Netanyahu put a political spin on the news while on a visit to Lithuania's capital Vilnius.
"That's good," he told reporters. "More should follow, more will follow, because Iran should not be rewarded for its aggression in the region, for its attempt to spread terrorism."
Dutch airline KLM, which is part of the same group as Air France, announced last month that it was suspending Tehran flights due to "negative results and financial outlook".
The airline said it was discussing rebooking options for customers with partner airlines and would offer full refunds if they fail.
Lufthansa and Alitalia are among European companies still running flights to Iran despite the US announcement.
Other companies pull out
Air France revived its service to Tehran after the nuclear deal was signed in 2015.
The other parties to the nuclear deal - Britain, France, Germany, China and Russia - have vowed to stay in the accord but the threat of US penalties has persuaded many companies to stop doing business in Iran.
French oil giant Total announced it had dropped a multi-billion-euro gas project and Air Liquide has also pulled out.