Talk to Verizon, tell them you are going abroad for an extended period. They should then unlock your phone so you can use a SIM card you can buy in Europe. Verizon will probably try to talk you into one of their SIMs for international travel but the ones in Europe are much cheaper.
Alternately, you can buy an international phone with a SIM or just the SIM card if your phone is International frequency capable.
I kept my old Blackberry, unlocked it, and installed a SIM from Mobal based in the UK. No data, which is fine by me, but you can use the phone anywhere in the world.
Per call charges are a bit steep but it works everywhere no matter what and there is no monthly (or even yearly) cost. Just fire up the phone and call, put it back in your suitcase when you get home.They bill you at the end of whatever month you make a call with the phone for the call time charges only, and don't bill you any month you don't use the phone.
It's a great backup or emergency phone ... even in North America. It connects to the nearest tower regardless of provider. It willl work every time anywhere on the planet where any tower is within range.
If you want data, or expedt to make a lot of calls, you should look at the European SIM option though.