Jacqueline Bisset On 'Extraordinary' Goddaughter Angelina Jolie & Being Cut from Mr. & Mrs. Smith

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Jacqueline Bisset's connection to Angelina Jolie began before Jolie was born.

The English actress, now starring in Amazon's Birds of Paradise, was close friends with The Eternals star's late mother Marcheline Bertrand, whom she met when she was costarring with Jolie's father Jon Voight in the thriller The End of the Game.

"I met her around 1971 when I was making a movie with director Maximilian Schell and Jon Voight, who [Bertrand] was married to at the time," Bisset, 77, tells PEOPLE in the latest issue. "We became friends, and she asked me to be her godmother when Angie was in the tummy."

Recalling the happy moment with Bertrand and Jolie captured in the photo above, from the Los Angeles premiere of Jolie's movie Original Sin in 2001, Bisset says their coordinated ensembles were a complete coincidence.

"We all turned up wearing white dresses, and it was absolutely unplanned," she says with a smile. "Completely unplanned. That was actually goofy that we're all wearing white."

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For much more on Jacqueline Bisset and her 50-year career, pick up the latest issue of PEOPLE on newsstands Friday

Although she is protective of her goddaughter, there is genuine pride in her voice when she speaks of Jolie.

"I find her rather extraordinary," says Bisset. "Her whole aura is breathtaking, and it's amazing how much she's changed in different stages [of life]. She's evolved so much."

The two actresses are very close and once almost starred together in the same film: Jolie's 2005 action/spy thriller Mr. & Mrs. Smith.

"The first film I got cut out of was [Mr. & Mrs. Smith] with Angelina," says Bisset. "Terence Stamp and I played Angelina and Brad Pitt's bosses. They were very small parts, but it didn't work [in the film], and then they recast it, with apparently two other actors. They said we were too British."

In the deleted scene above, director Doug Liman explained that they originally wanted the main characters to confront the film's actual villains, first played by Bisset and Stamp above, and then recast with Angela Bassett and Keith David. Both versions were scrapped.

Bisset, who has more than 100 film and TV credits under her belt, says that experience taught her a great lesson about choosing her projects carefully, so as not to be cut from one again.

"You have to try and find a role, even if it's a small role, that is absolutely integral to the plot," she says. "Otherwise you'll be on the [cutting room] floor."

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Currently co-starring in the elite dance school drama Birds of Paradise, the actress says she still has plenty on her acting to-do list.

"I get a real buzz from working and I enjoy being around people that I wouldn't meet otherwise," she says. "There are lots of things I'd like to do and I'd like to work with lots of people. I like Robert De Niro, very much. I don't know what show I would be put in with him. I'd probably be put in as his mother."

Birds of Paradise is now streaming on Amazon Prime Video.