Advice needed on Connection time at Lyon Part Dieu station

That should be plenty of time, but do be at the door of the train before the train stops at Lyon, ready to jump off with your luggage when it does. Try not to be at the end of the line, so you preserve all your time. If your intention is to catch the 8:38 departure there, then the next one is at 10:38. The only part of that day's ride that is reserved should be the first leg by TGV.

Thank you Laura for your advice. Yes, the connection to Bellegarde was for 8:38 am. I want to clarify my understanding of your response, though. If I don't reserve the ticket for the next leg to Bellegarde, then I need to stand in line in the Lyon train station to buy the next ticket. Which I am thinking would make it impossible to make the 8:38 am connection. Is that what you are saying?

No, get the whole ticket or two tickets before you board the first train. ..

The train after Lyon is an open seated train, no reservations offered or accepted. Don't wait until Lyon to get those tickets or that time WILL evaporate.

Thank you Nigel :)

Part-Dieu is a modern through station with platforms on an upper level and a miniature shopping mall underneath. The platforms aren't far from one another and there are elevators and escalators between levels. If you book all your tickets in advance a 13 minute connection should be fine.

Thank you Philip. It sounds like we will be able to do this if we are ready to go as we arrive in Lyon.
Also, I think I finally understand how the tickets work. On capitanetrain.com when selecting the tickets for the entire trip (reserved and non-reserved), it automatically picks the next available train on the next leg of my itinerary. So if we don't happen to make the 8:38 train, then I don't need to go purchase another ticket from Lyon to Bellegarde, I just get on the next available train (the 10:38) to Bellegarde.
Thank you everyone! I am from a small town, with no train service, so the logistics of changing trains is new to me. It sounds like it will not be too difficult.

I just dived deeper into capitainetrain.com FAQ, and of course there is my exact question.
I discovered that Lyon Part Dieu is covered by Railteams’s HOPNAT (Hop On The Next Available Train) service, which means I don’t need to purchase another ticket—just take the next train with my existing ticket.
I discovered this is not always the case, and it depends on the station. They have a list of stations where this is acceptable.

Again, I appreciate everyone's assistance.

I hadn't heard of this specific Capitaine Train service, but usually there's no problem with using tickets on a later Regional train anyway, it's the long-distance expresses where there's strict enforcement of what journey you use.

The 8:38 originates at Lyon Part Dieu, so it will be waiting on the platform when you arrive. Since these are regional unreserved trains, you will generally have that option, but in your case the options are limited. The next available train is at 10:38, then nothing (except passing through Switzerland, which you can't do with your ticket, or by bus) until 17:38, getting to Chamonx at 21:50.
The 8:38 and 10:38 have 2 hour changes in Bellegarde.