Simon Cowell Holds Hands with Pregnant Lauren Silverman

08/24/2013 at 05:00 PM EDT

Simon Cowell Holds Hands with Pregnant Lauren Silverman
Simon Cowell and Lauren Silverman
That's one happy father-to-be!

After admitting that things in his life were changing for the better, a beaming Simon Cowell held hands with Lauren Silverman, who is expecting his child, while walking along a French beach on Saturday.

It was the first time the couple have been seen together since news of her pregnancy broke. The X Factor judge is set to become a first-time dad with Silverman, who came to a quick divorce settlement with her husband, Cowell's pal Andrew Silverman, just two weeks after the pregnancy bombshell.

"I'm proud to be a dad ... It's something I hadn't thought of before, but now I know I feel good about it," Cowell, 53, said in a recent interview.

Whether or not Cowell and Silverman will ever tie the knot, a source tells PEOPLE that the pair, who are vacationing in the South of France, are definitely an item.

"They are making plans together," says the source, "for the future for themselves and the baby."

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