My wife and I took our Verizon cellphones to France and they worked without issue (the local network they used is Orange).
However, one day I got a text saying I had used up my daily high speed data allowance. Even though I'm on an unlimited plan, apparently when travelling you are limited to 0.5 GB a day, after which they throttle your speed. However they are more than willing to accept $10 for an additional 0.5 GB to use during your daily session.
I was surprised we used so much data in one day, we weren't using Google Maps or any local apps, I think maybe one of our phones was doing something in the background. So beware, if you think this might be an issue you could bring an old phone and buy a Carte Holiday SIM from Orange that would give you tons of data and a local phone number. I was going to do that but didn't find I needed it, our hotel room had wifi like all do so we were using that all the time we were in there and in stores like Galerie Lafayette and Printemps they had their own free wifi so I used that.