I am thinking that maybe there are buses that pass through but I'm not sure how to find them.
You should definitely try blablacar, as pointed out by mts in the comments.
It is much used in the Vallée du Rhône, I'm sure you will find a friendly driver.
If you don't find your route directly on the website, try broadening the start/finish of your trip by looking on a map.
I used blablacar a lot as a driver, unfortunately not in this area.
Also, if you do these trips regurlarly, there might be some subscriptions with the SNCF that could lower the price per journey.
tl;dr On Saturdays (or every day during school holidays), groups of 2-5 people can get a 40% discount if the ticket is bought using the SNCF phone app (but not with the OUI.sncf app). You need to explicitly select the discount in the app.
This applies to travel within the Auvergne-Rhône-Alpes region. Other regions may have similar discounts which the app should offer.
@Relaxed has mentioned the Illico Samedi discount for TER trains. Here's my experience with it:
There is a 40% discount (free ticket for children under 12) available for TER (i.e. regional) trains in the Rhône-Alpes region (thus also to Saint-Paul-de-Varax).
Conditions: there must be at least 2 people travelling (at most 5). No prior subscription is required (unlike with most similar discounts).
This is not a heavily advertised discount. More often than not, the staff at the station will not be aware of it. If you don't specifically ask for it, you will not get it.
It is not available from ticket machines (neither yellow SNCF or blue TER ones).
If you buy the ticket online, it must be bought on the Rhône-Alpes TER site and not the global SNCF site. It is not available from the latter. If you buy it using an app, you must use the SNCF app, not the OUI.sncf (formerly Voyages-SNCF) app.
I do not recommend buying the ticket online. If you do so, you must choose the time of travel in advance. If you buy it from the ticket office, it is valid for a certain number of days. You can just stamp it at the station and get on the train at whichever time you prefer. This flexibility is very important for me. UPDATE: If you do not buy it online, you may not be able to get it at the ticket office either. SNCF is terribly disorganized and they do not properly train their staff: often they don't know about this discount or do not know how to apply it.
At least in Lyon, be at the ticket office at least 20-30 min before departure. There may be big queues.