Jan 5, 2012 - 5:59 AM
It's quite hard to do that much traveling and also actually spend some time in the Alps. I'm not sure what kind of place you would like to visit. You can visit Geneva or Basel from Paris in one day, but these are not Alpine towns. It would take at least about another two hours to reach the higher peaks. I would suggest to check out the timetable
to see your options. Perhaps you can consider to visit Chamonix-Mont-Blanc. That's in the French Alps, but it should be possible to spend a couple of hours there and return the same day.
There is no cheapest route. With such a tight timeframe, you can best take any train that gets you to your destination most quickly. If possible, spending one night somewhere in Switzerland (e.g. Zermatt, Montreux or Les Diablerets) would give you more options.
I hope this helps. Please feel free to share further thoughts here.