Simon Cowell & Lauren Silverman — No More Hiding

Simon Cowell
, Lauren Silverman and their unborn spawn are making it official … stepping out together for the first time IN PUBLIC since news of their relationship broke.

The pic was snapped in the South of France Saturday — where the two are vacationing together amidst other rich people … looking carefree and happy.

Probably has something to do with that whole nasty-divorce-settled thing.