I recommend starting your search through AutoEurope, which gives comprehensive driving guides for rentals in Europe.

Your rental could be with one of the car rental companies mentioned above, or with a different rental company.

You will not know, in advance, which car rental company you will recieve a reservation with. The AutoEurope reservation guidelines state:

Auto Europe has arranged your rental with the car rental company shown on the voucher after your payment of the services. Auto Europe is independent, not an agent for any particular car rental company. This voucher confirms your reservation with the rental company. The voucher is not a rental agreement. When you pick up the vehicle, you must sign a rental agreement provided by the rental company and subject to local laws. Additional fees may apply for rental service beyond hours of operation. All car rates are guaranteed in US Dollars , all local fees are billed in local currency.

You can visit AutoEurope.com or AutoEurope.ca (for Canadian Residents) and check into the Guidelines for renting in Switzerland.

Here are the basics guidelines that are listed for Zurich rent a car:

General Information

Most car categories can be driven anywhere in Western Europe without restriction. Due to insurance regulations, there are restrictions on luxury car categories and on travel in certain countries. Auto Europe has special rental programs for driving into Eastern Europe. Make sure to ensure that your intended itinerary will be possible with the car you plan to rent.

Restricted Countries

Cars rented in Switzerland are generally not allowed into the following countries: Albania, Bosnia, Belarus, Bulgaria, Czech Republic, Croatia, Estonia, Greece, Hungary, Latvia, Lithuania, Macedonia, Montenegro, Poland, Russia, Slovakia, Slovenia, Turkey, Ukraine and Yugoslavia. Luxury cars are not allowed into Italy.

* NOTE:For an additional fee, travel into most or all of these countries can be arranged for specific car categories with advance notice.

If you do plan on traveling into any of the countries listed below, certain restrictions and fees may apply. Fees normally are 20% to 30% more than rates, but vary by location.

Albania, Belarus, Bosnia, Bulgaria, Croatia, Czech Republic, Estonia, Greece, Hungary,Latvia, Lithuania, Moldova, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, Turkey, Ukraine