Street said her parents wanted to give the men the benefit of the doubt, but then things got worse.
"Juliette goes down the fireman's pole. She's in her short little unicorn dress about to go down the pole. As she goes down the pole [the man filming her] says, 'Hang on, wait, three, two, one ...'
"He's filming her going down the fireman's pole. A complete stranger, (with) a group of three or four men, drinking heavily."
Street said her mother's "blood started to boil". When she complained to bar staff, they told her that the men were being kicked out after causing problems earlier.
They also told her that the man had denied filming Street's kids and explained that he'd been "FaceTiming my wife". He also said he hadn't saved the clip.
But Street said after the men were kicked out, "the one that was filming tore off in a huff and was stalking around outside the pub".
Street told her co-hosts it was her first time as a parent that something like that had happened to her and her kids.
"Why on earth is a man in his mid-40s filming two little girls in a playground? What possible excuse could you have?" she said.
"It just made me shudder ... It's scary. I can't believe it happened."
A police spokesperson told the Herald they weren't aware of "any other issues of this nature".
Street and France are expecting their third child, via a surrogate, in August.
Street announced on Instagram that she was unable to carry another baby herself due to her battle with the auto-immune disease Churg-Strauss, but her friend Sophie Braggins was carrying their "precious bundle".
She wrote: "We're extremely lucky to have such a special and selfless friend offer to be a surrogate for us."
