Hazel, Jarrod has some great advice for you. Get over the pond, and then make your connection! Lufthansa has some great direct flights from SFO to Frankfurt, and then they offer lots of times for flights to Venice. (We love flying Luft)
Last June we flew Luft over the pond into FRA, and then took them to Rome. We got a better price by booking the FRA to Rome trip ourselves (and more flight options!).
FRA,Munich, and others, are wonderful airports to make a connection. All of the flight agents speak excellent english, if that is one of your concerns. Sometimes we look for overnight options in FRA, ......beautiful old town, great restaurants, easy 15 min train trip from the airport to downtown (like BART), and the some very reasonably priced hotels. We did an overnight in Munich once. We stayed in a major chain hotel in a small town 5 min from the airport.......it was fun!
Plug the different european destinations into your airline search engine, and look at all of the options