"They spend time together in different places whenever they can," says a source

By Melody Chiu
Updated October 22, 2015 09:55 AM
Credit: David M. Benett/Dave Benett/Getty Images; UPI /Landov

There’s no city more romantic than the City of Light.

Earlier this month, Chris Martin and Annabelle Wallis landed in Paris to kick off a cozy weekend together. The new couple was spotted shopping around town and swapping kisses as they danced and strolled down the streets.

“They were very affectionate,” says one onlooker. “They were laughing and seemed like a very genuine couple.”

But while Martin – who split from on-and-off girlfriend Jennifer Lawrence earlier this summer – is getting closer to Wallis, they are still getting to know each other.

“He’s a nice guy just having fun,” says a source of Martin, whose ex-wife Gwyneth Paltrow is dating producer Brad Falchuk. “What woman wouldn’t like that?”

When they do reunite together, they keep things low-key. “They spend time together in different places whenever they can,” says another insider of Martin and Wallis, who were first spotted together in August.

For more on the new couple’s relationship, pick up the latest issue of PEOPLE, on newsstands Friday.

Reporting by Peter Mikelbank