She’s clearly lying to you, she’s not french.
Having said that, I’m surprised by how many people don’t know the proper word “monocycle” here. I’ve heard countless times from passers-by: “Check this out kids, a monoroue !”. Nope sir, it’s not called a uni-wheel…
I have noted that this confusion is generally due to our big wheels: a classic 20" or 24" is identified as a circus object thus people tend to know the correct word - “monocycle”. However, a bigger and larger wheel - typically a mountain unicycle - is not recognized as a circus object so people don’t relate it to this famous circus object.
As far as I know, “monocycle” is correct. It’s also true that many are unaware of this term because it’s not in common use. Many people end up using the English word unicycle because they don’t know the correct term, and with the Internet spreading English around the world, more people know the English term. Unicycling would be “faire du monocycle”. “Un vélo avec une roue” is basically “a one-wheeled bike”, and “velo avec une roue perdue” would be “bike with one lost wheel” - amusing, but incorrect.