Asked by PEOPLE about the split at the Cannes Film Festival on Friday, Simpson replied: "I am very happy, but I don't really want to talk about my personal life tonight because it's not what it's about. But I am very happy. I will let you know that."

The singer-actress officially announced her newest film project, Major Movie Star, at the festival Friday.

Simpson, wearing an off-the-shoulder sequined dress, arrived at the Budweiser Select yacht at 10:15 p.m. in Cannes to help promote her new role in the upcoming military caper, which starts shooting in July in Louisiana.

Earlier this month Simpson's rep confirmed to PEOPLE that the singer had signed on for the title role in the comedy, about a down-on-her-luck actress who enlists in the Marines.

Earlier Friday, sources close to both Simpson and Mayer confirmed that the couple had parted ways ¨C but not necessarily for good.

"They have broken up," a source tells PEOPLE. "But they have broken up and gotten back together at least 10 times before."

Another source said the pair have "been e-mailing and talking to each other" since Simpson arrived in Cannes on Wednesday.