I hate to contradict others, but here in the US, Verizon is not exclusively CDMA any longer. Their new LTE networks in the US are using the GSM network. Here in the states, Verizon owns both GSM and CDMA towers. Over time as they build their network, they will be moving to GSM exclusively.
It used to be that Sprint and Verizon towers used CDMA technology (does not work in Europe), and AT&T and T-Mobile towers use GSM technology (which works in Europe). At this point in time, Verizon offers both. That's why, years ago, if you switched carriers here in the states you often had to get a new phone, even if it was the same model. The 'innards' have to built to work on either the CDMA or GSM network, even if the exteriors look exactly the same. (I happen to work for one of these groups, which is how I know all of this. I promise I not a network guru, however: this is pretty much the extent of my knowledge on the subject. I've been lurking on these boards for months, but had to finally register today to correct the misinformation here.)
If your particular phone can connect to the GSM network, then it will work in Europe. So it's worth calling again (and again, if needed) to determine the towers your particular phone connects to. If they tell you it's a CDMA phone, then you're out of luck -- it can't connect to cell towers in Europe. If it's a GSM phone, then it can connect to the cell towers there and you need to determine if it's worth it to you, cost-wise, to bring it. If it's an older/cheaper phone, it is likely CDMA, but it's definitely worth investigating.
Good luck and happy travels!