Data privacy watchdog the CNIL said both sites were making it difficult for internet users to refuse the online trackers.
The social-media firms have three months to comply or face penalties of 100,000 euros for each day of delay.
Cookies are little packets of data that allows web browsers to store information and provide, for example, targeted ads.
“When you accept cookies, it’s done in just one click,” said Karin Kiefer, the CNIL’s head of data protection and sanctions.
“Rejecting cookies should be as easy as accepting them.”
In its statement, the Commission Nationale Informatique & Libertés said it had found that while the tech giants provided a virtual button to allow the immediate acceptance of cookies, there was no equivalent to refuse them as easily.
Google, which was fined 150m euros, said: “People trust us to respect their right to privacy and keep them safe. We understand our responsibility to protect that trust and are committing to further changes and active work with the CNIL in [the] light of this decision.”
Facebook, now owned by Meta, said it was “reviewing” the decision to fine it 60m euros.
“Our cookie consent controls provide people with greater control over their data, including a new settings menu on Facebook and Instagram, where people can revisit and manage their decisions at any time, and we continue to develop and improve these controls,” it said.