Credit: INFphoto.com Photo: Simon Cowell and Lauren Silverman Seen in Saint Tropez on August 25, 2013

Now that Lauren Silverman’s divorce has been settled and she’s flown to the south of France to join baby daddy Simon Cowell on vacation, the two of them are thrilled to no longer be hiding their affection.

“They’re really enjoying being able to be out and about as a couple,” a source tells Wetpaint Entertainment. “They’re in love and really excited about the baby.”

But as Wetpaint Entertainment previously reported, Lauren will not be moving to Los Angeles to be with Simon once their vacation ends.

“She can’t,” the source tells Wetpaint. “Her son Adam is in New York and she’s not about to leave him. What will likely happen is she will travel to LA from time to time when Adam is with his father. Otherwise, Simon will come to NYC.”

Indeed, while Lauren has been with Simon in France, Adam has been staying with his dad, Andrew Silverman. Andrew and Lauren had been married ten years and just settled the terms of their divorce last week.