Matt Baron/Shutterstock, Pascal Le Segretain/Getty Elle Fanning; Tom Cruise
Speaking to the audience at the premiere of his new movie Top Gun: Maverick Wednesday at the Cannes Film Festival, Cruise, 59, praised Elle, 24, while sharing an early memory of the "very talented actress."
Elle — who smiled widely from her seat during Cruise's speech — told PEOPLE after the event that she "was freaking out" and "sort of crying/blushing" during the sweet moment.
"I was waking up pinching myself. Did that really happen last night? Was I dreaming?" adds the actress and L'Oréal Paris International Spokesperson.
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Andreas Rentz/Getty Elle Fanning
During his speech, Cruise praised Elle and Dakota, 28, for their acting talent and ambition at a young age, after first meeting them as children.
"[Elle's] going, 'I'm an actress,' and I said, 'I know you are," he said. "I was working with Dakota, who's a genius, and I was there with Elle, so I said, 'What are you gonna do?' She was like, 'I'm an actress, too.' I was like, 'Yes, you are.' "
Elle tells PEOPLE that Cruise "made it a point to kind of stay in [Dakota's] life" after they finished filming War of the Worlds, "which was so kind."
"And he sends her a birthday gift every single year still," Elle says. "We get the coconut cake that he sends, which I know Kirsten Dunst said she gets one, as well, from working with him in Interview with the Vampire."
Lester Cohen/WireImage Tom Cruise and Elle Fanning
"I think it just shows how even the younger actors — he wants to be out there and inspire young actors to keep going," adds The Great star.
Elle also shares with PEOPLE that she used to hang out on set with her sister on films like War of the Worlds and Man on Fire, making crayon drawings for Cruise on the former and Denzel Washington on the latter.
"I remember my photo [I gave Tom] was of one of the War of the Worlds things — it was my sister and him running away. It was a crayon picture. That's my memory of meeting him," Elle says.
"And he said he remembered. It seems like he does!" she adds.