Drew Barrymore (left) and an unidentified companion in Paris
03/14/2012 at 09:00 AM EDT
and her fiancé Will Kopelman
are playing tourists in Paris this week, shopping and sightseeing around the city.
Barrymore, 37, who is rumored to be pregnant
, donned her nearly 4-carat engagement ring
as she spent more than two hours Tuesday at Chanel on the Right Bank.
(This could be Drew's big chance for a dream shopping spree, because Kopelman's father is the former president of the fabled fashion house.)
While she was in and out of the stores, Kopelman perused art galleries on the Left Bank's Rue de Seine.
Tuesday evening, the recently engaged couple
enjoyed a romantic dinner at Chez Georges, a classic 1950s style bistro on Rue de Mail.
On Wednesday, Kopelman went for an afternoon jog while Barrymore headed for the St. Michel district.
Reporting by PETER MIKELBANK