06/13/2010 AT 4:00 PM ET
Is Kate Hudson dating another rock star?
The actress hopped a plane to Paris over the weekend and attended the second of two sold-out shows for the British rock band Muse Saturday, standing in an audio tent amid a crowd of 80,000 at the Stade de France.
The next day, she was spotted around town with the band’s frontman, Matthew Bellamy, who is a singer, guitarist and songwriter.
The pair were seen strolling through the Place Vendome, a square in the center of Paris. “They seemed very much a couple,” a witness tells PEOPLE. “Just walking together, enjoying the sunshine.” Later that afternoon, Hudson and Bellamy opted for a late lunch on the Left Bank at the celebrated Brasserie Lipp, leaving through a rear exit of the eatery when photographers turned up outside.
Hudson was most recently linked to the New York Yankees’ Alex Rodriguez, but their relationship ended late last year.