The couple, who revealed their engagement in March 2012, are planning to get married this weekend, a source confirms to PEOPLE. They boarded a flight to Paris Tuesday with Berry's daughter, 5-year-old Nahla.
With rumors flying of an impending wedding, whether they remain in Paris or travel further afield – Martinez loves the Mediterranean – remains a mystery. But the pair have had their eye on summer nuptials for some time, several sources say.
Berry, 46, and Martinez, 47, who are expecting their first child together in early fall, are frequent visitors to the City of Light.
Most recently, the pair attended the Champs-Elysées Film Festival in mid-June, where native Parisian Martinez revealed that the pair would be welcoming a boy.
"My son will be an American," the actor told PEOPLE.
An item since they met on the 2010 film Dark Tide, "they seem truly in love," says Sophie Dulac, president of the Champs-Elysées Film Festival. "I've known Olivier very well and have never seen him like this."
Likewise, Berry has been head-over-heels for her French amour – and his homeland.
"She has called him 'The One,' " says Dulac. "She's said she never expected to meet this Frenchman, to fall in love like she has."
It will be the first marriage for Martinez, who previously dated singer Kylie Minogue, and the third for Berry, who was wed to baseball player David Justice in the early 1990s and to singer Eric Benét in the early 2000s. She also weathered a protracted custody battle over Nahla with her most recent ex, model Gabriel Aubry.
In 2007, the actress told InStyle she had sworn off marriage: "I will never, never get married again."
But when Martinez proposed with an emerald engagement ring by Paris designer Robert Lazlo in early 2012, Berry was ready to say "oui."
In April, Berry revealed her pregnancy, which she has called "the biggest surprise of my life."
"Having a baby brings them closer and gives them that much more to share," a source told PEOPLE this spring. "They are very much in love."
But before baby makes four – a wedding.