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October 18, 2015 08:00 PM

Chris Martin and British actress Annabelle Wallis kept their romance light and playful as they walked around Paris hand-in-hand on Saturday.

The pair, who were first spotted together in August, were openly affectionate as they embraced and shared several kisses.

Wallis, 31, of The Tudors and Peaky Blinders, beamed as she and Martin chatted and dance around the French capital’s streets.

Despite Wallis and the Coldplay crooner’s PDA, a source tells PEOPLE that Martin isn’t looking to immediately settle down after splitting from actress Jennifer Lawrence in August.

“He’s a nice guy, just having fun. What woman wouldn’t like that,” the source says.

Martin, 38, was married for 10 years to Gwyneth Paltrow before they “consciously uncoupled” in March of last year. The two have remained close, often spending time with their children, Apple, 11, and Moses, 9, together.

Annabelle Wallis and Chris Martin
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Lawrence and the musician dated on-and-off over the past year, but broke up for a second time because, according to a Lawrence pal, she got “tired” of him “being so noncommittal.”

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