French countryside of Switzerland

Yes it should be fine. You could do Murten/Gruyeres on the 6th then find a hotel in Vevey or Montreux. On the 7th do Montreux/Chillon and drive at night to Zurich (~2 hour drive but depends on road work). Make sure to stop by the 12th Century Lavaux vineyards from Gruyere to Montreux. It should be gorgeous in October. I personally would book hotels in advance to benefit from better deals (Priceline, Hotwire etc...) and for my peace of mind.
Also be aware that the speed limit is strictly enforced and there are automatic speed traps in many locations (depending on the Canton).

Irma, Could you double-check your dates, please? You said you arrive on October 4 and leave early on the 8th but will be back to Zurich the night of the 8th.
Do you mean you are flying to Zurich to spend only 4 nights and 3 full days?

Darcy, sorry. We need to be back in Zurich in the evening on the 7th as we fly out very early on the 8th. This will be at the end of 2 week Rick Steves tour of Ireland and the 14 day Best of Europe.

Oh! that explains the short time! I was very concerned! It's been several decades but I loved Montreux but then I'm partial to Switzerland! (My favorites are Lausanne and Maienfeld.) I feel that since you'll have a car, you'll have the ability to change your plans as you go if you wish.

You can do that.... you may run into traffic both ways around Zurich. If you like chocolate there is a very interesting chocolate factory tour near Gruyeres. Park right outside. You might want study up on Swiss Zentrale-Parkuhr (spelling) blue parking meters where you need the number of your space and number plate details but no ticket. Be careful of your speed.

Yes, there's time. We were in the eastern part of Switzerland on our 2011 trip and (due to a change in plans) had one day to get back to the Geneva area, and it was no sweat. We even made a return visit to Gruyere on our way back. Don't need to make advance reservations, if you don't want to, we had no problems anywhere getting a place to stay, and we were there end of September.

When you rent a car in Switzerland--or I suppose any place in Europe--what do you do about liability insurance? I've read about collision waiver but what about the rest? I know car insurance here is only good for the US. Might it be better to get a transfer pass to Bern and rent a car there instead of renting one at the airport? Still working on the rent a car or use the train question....

Your credit card should come with an insurance for your car rental. I had an incident once in Switzerland and the credit card covered most of the cost. It was a bit of paperwork hassle but it worked okay at the end. The basic rental rate should include liability insurance to protect other people and their property in case you are the cause of the accident. Regarding renting in Bern, I do not see the advantage. The car rental place is inside the Zurich airport (no bus) so it is very convenient. I still would book my hotels in advance. There are sometimes major events (business, sports) in Geneva or Lausanne where all the hotel rooms along lake Geneva are booked. Maybe October is safe but I got completely stuck in April.
Be aware when you make a reservation that the cars have manual transmissions unless you specifically request a car with an automatic transmission.