Traveling input for Geneva > Chamonix > Paris?

So is there a train? Or is one of the transit services I've found online the best?

In the first instance - before going to the various national public transport websites - I suggest you try Google Maps under Directions (white arrow in blue diamond) - just enter Geneva and Chamonix, and any public transport services that exist will show - and there are some.

We use www.rentalcars.com to pre-book rental cars overseas .. it will show you all fees and charges, including drop-off fees, if any. Not certain you will be able to secure a car in Chamonix for dropping off in Paris - you might need to check in Annecy or possibly Lyon.

Can't assist on nice towns between Chamonix to Paris, but if you have a spare day in Paris, then a trip to the Palace of Versailles is recommended.

If you really like to experience Switzerland than not just spend one single day in Geneva, which is the least swiss city of them all.

Head to Lausanne or Montreux for the night and travel via Martigny and Vallorcine to Chamonix (yes. by train), then you can at least say you've travelled trough Switzerland. Maybe make it two nights and head up Rochers-de-Naye in Montreux and visit the castle of Chillon.

The train ride from Geneva to Chamonix is less than two hours and taking the train avoids the multi-country drop-off charge which will nick you for several hundred euros with a car rental. I agree with Onyx that Montreux with a visit to the Chateau de Chillon tops Geneva.
Nine days doesn't give you a lot of time. After a couple days in Chamonix, you really have just six days remaining. Lyon is a great city to visit- it's the culinary capital of France, has a lot of history, including a Roman amphitheater and a museum that has a Roman chariot on display. TGV trains connect Lyon with Paris in two hours. Lyon is 4 hours by train from Chamonix and is worth a couple nights which would leave you with four nights in Paris. Versailles can be reached by commuter train from Paris in less than an hour, so there's no need for a car to visit the Palace at Versailles.
Have a great Trip!

Maybe make it two nights and head up Rochers-de-Naye in Montreux and visit the castle of Chillon.

We visited the castle, and took the mountain railway up to Rochers-de-Naye, all in the one day - and I can second the recommendation.

I also recommend that you check well the train / bus connections Martigny > Vallorcine > Chamonix. I say this because we had some drama on our trip - with the train for the last leg into Chamonix not running that day, or not for many hours, or something (but we hitched a ride with some SAS soldiers in their Army truck).

Geneva - Chamonix: take the bus
There are actually 3 fast buses (1 hr journey) and 6 buses with intermediate stops (2 hrs journey) daily. Timetables change according to the season.
Rental car: you may rent a car in France, either at Geneva airport, French sector, or in French towns around Geneva, like Annemasse, Ferney, or so, all linked to Geneva by Geneva city buses.
With only 9 days, you will probably not have enough time to enjoy the gems between Chamonix and Paris.

I agree with @meckerdv -- your best options for Geneva to Chamonix are by bus transfer or by car. The driving time from Geneva to Chamonix is about one hour, depending on Geneva's traffic (which is often atrocious) and on your point of origin.

If you rent a car and you plan to drop it off in Paris then as @meckerdv suggests rent it from the French sector of Geneva airport. You won't find any national companies in the satellite towns around Geneva. But make sure the car comes with a vignette (prepaid motorway tax label) for use on Swiss motorways, and expect to pay quite a lot in tolls for the motorways in France. I live in Geneva but I have not driven to Paris, however I expect you will pay something like EUR 70-80 for the tolls on French roads on this route. When you add fuel costs the price of a TGV ticket becomes quite reasonable in comparison.

If you want to rent a car just for the journey between Geneva and Chamonix then look for a local company in Geneva, such as Patrick Location.

• http://www.patricklocation.ch/en

Dijon is a good place to break the long drive to Paris. A very scenic route from Chamonix is via the Col des Montets (FR) and then Vallorcine (FR), Martigny (CH), Montreux (CH) and Lausanne (CH) before heading off to Dijon across the Jura mountains. But travelling via Martigny also puts you in range of Zermatt and the Matterhorn, so if you are particularly ambitious you could look at that as a one-day/overnight side trip.

What you do in Geneva will depend on your interests. As for:

Geneva, which is the least Swiss city of them all

This sort of statement discounts the facts of modern Swiss history and the ethos of the Confederation, @onyx007. Geneva is definitively Swiss.

I fully agree with emmeff: Geneva is not less Swiss than Zurich, Berne or Jungfraujoch. Switzerland consists of 4 cultures, 4 languages, 26 small Republics called cantons with own governments, own legislations, own taxes etc. Geneva, the European seat of UN, the seat of the International Red Cross Commitee, etc. is just one of them. Every Canton is different, but all together form the Swiss Confederation. Switzerland wouldn't be Switzerland if it would be organized in another manner.

I fully agree with emmeff: Geneva is not less Swiss than Zurich, Berne or Jungfraujoch.

I think it's worth cutting onyx some slack here ... in a tourist/traveller context (where we are right here). Perhaps by "Swiss" they mean soaring snow-capped peaks, stunning lakes, beautiful green fields, Old-Town architecture, and small ski towns, or something like that.

Geneva is a modern city, and while no-one would deny its genuine Swissness, it's a bit like saying than New York is like the rest of America, which it clearly isn't in most of the ways that matter to the overseas tourist.

Anyway - I agree that if you can add the time to Zermatt (detour from Martigny then Visp) it's well worth an overnight.

Sunbird9 got my point; of course Geneva is Swiss (and it's nice), but it's (as we call it) not a "business card" for Swiss Tourism,as it is such an international city. If you're on a journey through Switzerland it's for sure a place to see, but if my goal is to visit Switzerland and have only a couple of day it would not be my first choice. Switzerland is not about the cities, but about the landscapes, nature and yes, soaring snow-capped peaks...

After all Geneva is home for at least 23 international Organisation including WHO, IKRK (the Red Cross) and the European Headquarter of the UN as meckerdv wrote. Over 43'000 people work for one of this organisation and this might be one of the reason, Geneva has the highest population of Non-Swiss People. Making it probably the ex-pat capital of Switzerland...