And now it looks like their romance is in full swing, with the pair spotted making their way through Paris’ Charles de Gaulle Airport on Tuesday after a romantic break in the city of love.
Arriving in the same vehicle, both attempted to go incognito in shades, despite the gloomy December weather.
Dakota, 28, wore her brunette hair long and loose, while Chris, 40, bundled up against the cold in a grey scarf and a black beanie.
In November the Fifty Shades actress was spotted sitting with the crew at a Coldplay concert in Argentina before they headed to a Nick Cave concert in Israel together.
And a source recently told Us Weekly that they are more than just a fling.
“Dakota and Chris are definitely dating,” said the insider.
“They’ve gotten to know each other really well and are very comfortable from one another. Chris sends Dakota his music to get her opinion. It’s more than just a fling.”
An onlooker who spotted them at LA’s Sushi Park back in October said they walked in together and were ‘tucked away’ on a table in the corner.
“They seemed very happy to see each other and immediately jumped into conversation,” a source told Us Weekly.
“Chris was very charming and personable. His face lit up when he was talking to her. He hummed a little bit and asked her what she thought of a song.
“She clearly loves his music and was really into it. They were flirty and laughing the entire meal. He paid for dinner and held the door for her. They both thanked the chefs on the way out.”
Chris was previously married to actress Gwyneth Paltrow, who he has 13-year-old daughter Apple and 11-year-old son Moses with.
Mirror Online has contacted reps for Chris and Dakota for comment.