The exact same thing is observed in Belgian French (wallonian) where they use "une fois" (same thing as "once") because of the dutch speaking influence locally.
Also in standard mandarin, where you can soften an imperative (I am told that the intuition is that the duration of such a modified verb is short) by adding 一下 "one time".
As far as I know (not authoritative), the construction is native.
"Une fois" means "once" in standard French ("il y avait une fois..."). Is there a specific context you're thinking of where it's used in a non-standard way?
Oh, you mean like "Donne-moi une fois quelques minutes" - the exact same construction as the parent was pointing out exists in Wisconsin. Fascinating. Thanks for clarifying.