NEWS UPDATE: Cheryl IS married in secret ceremony!
The source elaborated: "Their relationship has really hotted up, and he's a very impulsive guy.
"It's only early days but Jean-Bernard isn't shy about admitting his feelings and has told Cheryl what he wants.
WATCH! They DID tie the knot!
"He thinks the two of them are perfect together and would love to marry her. To people who don't know him it might seem rushed but he's a passionate Frenchman – he wears his heart on his sleeve."
Indeed, the pair seem smitten after meeting just three months ago at the Cannes Film Festival, where Jean-Bernard runs restaurant, Cosy Box.
The friend elaborated: "There was a time when many of her friends thought she'd been put off marriage for good, but [Jean-Bernard]'s totally turned her around. It's great to see her so, so happy."
"She really seems to think he's the one, and her friends haven't got a bad word to say about him.
"He seems absolutely perfect, and they're great together. Obviously it's still early days, but this looks like it's set to last."
And he's already proven he's great at big gestures, gifting Chezza with hundreds of roses last week for her 31st birthday.
But as to whether a wedding is imminent, we'll have to wait and see.
WATCH: They DID tie the knot!
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