The actress was on hand Saturday at Cannes, where the the Palme d'Or was awarded to French filmmaker Justine Triet for her flick, 'Anatomy of a Fall' -- with JF announcing her as the winner and there to give her the actual prize ... a scroll/certificate with her name on it.

Watch ... after Triet accepted the award and gave a heartfelt speech, she started heading back to the nearby bleachers onstage where the rest of her team was, as she was prepared to give a round of hugs. Only problem -- she forgot the actual award at the podium!

Jane was right on it, grabbing the certificate and briefly running after Triet to flag her down so she could take her paper hardware with her, but it doesn't look Triet heard her at all.

After quickly realizing it was a lost cause and that Triet wasn't coming back for it anytime soon, Jane stopped in her tracks and chucked the thing at her ... and it made contact. 😅

Everyone in the audience saw it, and the moment was actually captured as part of the broadcast. Funny enough, a gent standing right there picked it up and also tried to giving it to Triet -- but even he was unsuccessful in getting it back to her. She was in the zone!

No harm, no foul -- the certificate is as light as a feather and it doesn't appear she even felt it hit her back when Jane threw it at her. All in all, it was hilarious ... and oh so very Jane.