Many thanks to JustinLennox for sharing the story of his family’s Keanu encounter on reddit and their photo with Keanu on imgur. Based on the hotel and Keanu’s appearance, the photo was taken during the Something’s Gotta Give shoot in Paris in June 2003. Their story is below.
… I was on vacation with my family in Paris and we had just climbed the Eiffel Tower. When we came back down my mom swore she saw Keanu go into a trailer nearby and she got super excited. She went and knocked on the trailer door (to much protest and embarrassment on our part), and a man that was definitely not Keanu came out. My mom asked if Keanu was in the trailer and he said yes but Mr. Reeves had had a long day of filming and was very tired. And then Keanu comes out and is like “No no it’s fine, always nice to see some friendly faces”. And then he says, in the coolest and chillest manner which my mom quotes to this day and has become a joke within our family— “How’s that jet lag treatin you?”— just dripping with swagger. He was incredibly nice to us and down to earth and took a picture and even signed a random piece of paper from our hotel.