Budget friendly visit to Switzerland with a baby

To get the best answer to your question I need one piece of information:
How are you arriving in Switzerland (where, and by what method of transport, car, train, air, boat)?

You said "where is the best place to take off going to Paris?". But, if you are going from most parts of Switzerland to Paris, flying is not the best way. It is quicker, and a lot more comfortable, to take the TGV (High Speed Train) from Geneva, Lausanne, Zürich or Basel to Paris. If you insist on flying, airports are Geneva, Zürich or Basel.

"Which city or region has the cheapest accommodation?" - It doesn't matter where you stay, prices are similar. You don't want to be staying in a city, you want to be in the mountains.

For 3 nights, I would recommend either:
1) Luzern. If you want a town to stay in. On a lake, with boat trips, and mountains to go up (Pilatus, Rigi and Titlis)
2) The Jungfrau region. One of Wengen, Lauterbrunnen, Mürren or Grindelwald.

"What would be the weather in Switzerland on those days? Should we bring winter clothes?" - weather is determined by altitude. In the valley, where you will be staying, you need a jacket. And there may be rain. If you go up mountains, expect snow at the top. Titlis and Jungfrau have permanent glaciers. So bring an extra layer.

Hi Chris!

Thanks for your response.
How are you arriving in Switzerland: we’ll be arriving at Zurich by plane then we plan to go to Paris
I’m thinking of 4days 3 nights visit in Switzerland then off to Paris. And yes, we are planning to get to Paris thru train. Do you suggest we book ticket going to Paris in advance? Which route/station is most accessible?
You are right with the accommodation, We just want to enjoy the beauty of nature and the best of Switzerland. Though, which is baby friendly in terms of accessibility to places I want to visit?
And should we buy the family pass?

Thank you

Jessica, both places I suggest (Luzern or Jungfrau region) can be reached by train from Zürich airport.

Swiss trains do not need reservations and (mostly) do not have discounted advance tickets. French high speed trains, including those from Switzerland to Paris do. And you get large discounts for advance purchase.
Therefore buy your ticket to Paris as soon as you are prepared to commit. This ticket will include reserved seats on the trains and will only be valid on the train listed.
From both Luzern or Jungfrau region, the quickest route is to take a train to Basel, and catch the high speed train there.
You can look up times and buy tickets on the SBB website: https://www.sbb.ch/en
Just enter Wengen (or wherever) to PARIS, date and time.

I am chickening out of the baby question. Trains are baby friendly, and modern trains have changing facilities. No seat restraints needed.

Not sure what you mean by a family pass. Whether you need a pass depends on how many mountain railways and cable cars you will be using.