I was reading "From Paris to the Moon" before our upcoming trip to Paris and the author mentioned the winter circus in Paris which I thought sounded interesting.

Is it like Cirque du Soleil? Or more like Barnum Bailey with live animals and such?

Is this a popular event where I should be purchasing tickets before we go?

Thanks!

The "cirque d'hiver" is actually a building, not a circus like the "cirque du soleil" (it originally was when it was build, though). It displays various shows, sometimes circus, but usually totally unrelated events (for instance, by gooling it, the two first shows I saw mentionned were an humorist and turkish wrestlers)

I'm afraid my French is not so good but when I pulled up this website it looked like a circus with clowns and acrobats.

www.cirquedhiver.com

We will be there in late December and it looks like there is an actual circus at that time. Can anyone confirm this?

http://www.veress.se/cirquedhiverbouglione.htm

this site might be easier for you.
As clairobscur said, the building is used for shows and entertainment. In January for a couple of weeks, they put on circus-like shows. Bouglione is this years entertainment.

Yes, the event runs until early February and you can look through the website to find the location near Rue Oberkampf (click: acces) along with finding the performance times and ticket prices. They were busily putting up colorful signs promoting the upcoming spectacle over the Thanksgiving weekend, but I really don't know anything more about it.