updated 01/21/2012 AT 12:55 PM ET
•originally published 01/21/2012 AT 2:50 PM ET
French actress-singer Paradis, 39, has spent the last few days in Paris, where on Friday she shopped in the Marais district and went for a fitting at Chanel’s headquarters on Rue Cambon.
While Paradis is expected at Monday’s Paris premiere of her film Café de Flore, Depp, 48, has been keeping a low profile in Los Angeles. He was spotted sporting a fedora and driving a luxury sports car Thursday, and he showed up later that night at the Hollywood Museum, according to sources.
He’s due in New Mexico next month to start production on his new movie, The Lone Ranger.