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.
Bellamy isn't the first musician to catch Hudson's eye. She was previously married to Chris Robinson of the Black Crowes, with whom she has a son Ryder, 6. Hudson and Robinson split in 2006
Hudson was most recently linked to the New York Yankees' Alex Rodriguez, but their relationship ended late last year.