Hi pheliayeo, and welcome to the forum! Based on your travel plans, my advice is to purchase either a Swiss Saver Pass or a Swiss Saver Flexi Pass. It wouldn't be cost effective to supplement this with a Eurail pass, or to buy a Eurail France-Switzerland Pass. Your stay in France is relatively short, and the trip from the Swiss border to Paris and back seems to be the only French journey you'll be making. Therefore, it wouldn't be economical to pay for a pass that covers travelling throughout France. Only very precise calculations
would give a definitive answer as to which pass is cheapest, but I hope that the information below helps you decide.
A 15 day Swiss Saver Pass
would cover almost all days of your stay and offers free travelling throughout Switzerland in trains, buses and boats on all days. Mountain trains and cable cars are discounted. Please take a look at the map under the link 'Overview of the network on which the Swiss Pass is valid' at the Swiss Pass page
to find out which routes are included. The Swiss Saver Pass is a convenient option, as you don't have to buy reduced tickets for your train, bus and boat trips. If you order a free STS Family Card along with your Swiss Saver Passes, your 13 year old child will traveling along for free. A Swiss Youth Pass can be purchased for your 17 year old child.
A Swiss Saver Flexi Pass
allows free travel on a number of days, which you can determine yourself. The maximum validity is 1 month and between the first and last day of free travelling, a 50% discount applies throughout Switzerland. The free travel days can be used for the longer and more expensive train journeys in your itinerary, such as Zurich-Lucerne, Interlaken-Zermatt, Montreux-Bern, and so on. On the remaining days, you'll profit from a 50% discount. This does require you to buy discounted tickets for your trips on these days. Again, your 13 year old can travel along for free with a free STS Family Card. There's no Youth variant of this pass, so a normal Swiss Saver Flexi Pass should be purchased for the 17 year old as well.
As for your other questions: train journeys between Geneva and Paris, and between Paris and Zurich, can be booked through this page
. Simply fill out Geneva as your departure station, Paris as your arrival station, and pick one of the connections offered by the timetable. Repeat the procedure for your journey backwards from Paris to Zurich. These international train trips have to be booked in advance indeed, and it's wise to arrange for this as soon as possible, as prices may be higher when booking shortly in advance.
I'm not sure which schedule you have in mind for December 22. There's quite a direct route between Zermatt and Montreux, and it would be a long detour to travel via Lausanne, Bern of Geneva. You can plan your trips using the Swiss timetable
I hope this provides some answers! Kind regards,