How do I discover what parts of France are within 1-day travel?

There is no single resource. It depends on the mode of travel. I suggest you start making a list with the place you are interested in. If you don't know yet, start with a map, pick some places and check.

The high speed trains (TGV) are quite efficient. You can check schedules here. There is also an international version of that site.

For more regional destinations (e.g. Versailles) check the Transilien website.

With the efficient train network, flying is hardly interesting. Nevertheless, it is still wort trying. Just check on Matrix Airfare Search what's available.

There is an intercity bus network in France, but it is not particularly relevant if you want to make a return trip in a single day. If interested, have a look at the list of companies who are serving Paris.

I would not do a return trip from Paris to Chamonix in one day. It takes least 5h30 to go there. An about the same to go back. On the other hand, you can consider taking the night train. It leaves Paris at around 11PM and goes to Saint Gervais. From there you can proceed to Chamonix by regional train. Arrival at 9:50PM. You can leave Chamonix at 7:14 PM to arrive in Paris the following morning a bit after 6AM.

Or travel during the day and simply spend a night in Chamonix, if you can.