Paris prosecutors said Musk and former X chief Linda Yaccarino were summoned for 20 April but did not appear for questioning.
The case stems from complaints that X manipulated algorithms to influence French politics and let Grok generate Holocaust denial and non-consensual explicit deepfakes.
The investigation, requested by MP Eric Bothorel, follows a raid on X's Paris office and comes as other jurisdictions, including California, also examine X and Grok.
Can French law hold a US tech mogul accountable for his AI, setting a new global precedent?
Why was Elon Musk's AI company dissolved just one day before French prosecutors called for charges?
With its original creators gone, who is now responsible for controlling the 'unrestrained' Grok AI?