Flying into and out of Paris

Look at http://reiseauskunft.bahn.de/bin/query.exe/en for train connections. Spell Zurich as "Zuerich" on this site, or else you'll get the airport stop instead of the city. You cannot get prices or buy tickets on this site for your routes, but this is the easiest one to use for schedules. Look at http://www.skyscanner.com/ for flights. Paris and Zurich are connected by direct trains every few hours, taking 4 hours. Buy ahead on the French or the Swiss rail site for best prices (this ticket will be very pricey if you wait until you get to Europe). You can also fly, but by the time you get to and from the airports and allow enough time for check-in, the train will be just as fast, if not faster. Vienna is the outlier; from Zurich by train it's about 8 hours, and from Paris by train it's over 11 hours. I'd look into flying; you may get a better price by buying a round trip ticket, and just discarding the return portion. Again, you need to book this as soon as possible, as flight prices go up closer to the departure date. When booking your trans-Atlantic tickets, be sure to fly open jaws (called "multi-city" on airline booking sites like Kayak and Expedia). For instance, fly into Vienna and out of Paris. Even if this is "more expensive" than a round trip to Paris, you save lots of time and money by not backtracking. To summarize, I'd fly into Vienna, fly from Vienna to Zurich, take the train from Zurich to Paris, and fly home from Paris. If you've already booked your tickets round trip from the US to Paris (as suggested by your thread title), see how much it would cost to change it, and compare this with the cost of the extra flight you would need to get from Paris to Vienna to start your trip.

Thank you for your advice. I am traveling on a free ticket and trying to do this low budget. I will probably just do Vienna on another trip.