No, you don't NEED a different SIM card to use it in France and the Netherlands, but it would be a LOT less expensive if you choose to do so.
If you use a local SIM card from those locations, you would be paying the local rates of the providers in those areas. You would also have a local phone number which you would need to give to anyone in the states with whom you would like to stay in touch. If you use your Verizon SIM card, you would be paying Verizon's extremely high international rates for all calls/texts/data you use while there. These costs can be seen HERE, but for France/Netherlands the calling rate starts at $1/minute and texts you send are $0.50 each and $0.05 each for those received. Data would be $25/100MB.
