Train Paris to Lyon/Lyon to CDG

As a general matter, your best option for getting to Lyon from Paris via is train is by catching the train at Gare de Lyon. Trains to Lyon and other areas south/southeast of Paris leave from Gare de Lyon or Gare de Bercy. There are local trains from Gare de Bercy but they take twice long. It is theoretically possible that there could be a train from another of the main stations but that would mean something major was wrong with a train line or with Gare de Lyon or Gare de Bercy. There are usually trains from Part Dieu to CDG. Are you searching on sncf-connect.com? Of course, the May 2023 schedule is not yet available but, schedules do not change much and looking at the current schedule would give you a good sense of what May's will be in

in common with many large European cities, there are several main stations in Paris (just like London) scattered about the city, but they are terminal stations (trains don't go through, they end and start there).

Each region of the country is served by trains out of only one (usually) of those stations. Fast trains to the southeast includung Lyon are only from Gare de Lyon.

Part-Dieu is in general the main station in Lyon, but all three stations are used.

Picking a random date in January, the 7:45 to CDG leaves Lyon-St Exupery and takes two hours and 6 minutes, the 8:30 leaves from Part Dieu and takes 15 minutes longer, the 9:04 completes the trio and leaves from Lyon-Perrache, taking 2:18. For one taking under 2 hours you want the 11:33 from Lyon-St Exupery taking one minute under the two hours.

Only the 9:04 originates in Lyon, all the others start further south and only call at the Lyon station for a short while.

I hope you are not planning to take one of these to the airport and hope to connect the same day for the flight home. That would be courageous.

It's most common for trains to CDG to depart from Lyon's airport (Saint-Exupéry) train station. It's possible you could find one leaving from Perrache or Part-Dieu to CDG, but those are less common -- trains departing from those stations typically head into Gare de Lyon in Paris. You can get to the Saint-Exupéry station by either cab or by Rhônexpress, a light rail that is less susceptible to traffic delays compared to taxis. It departs from the east side of Part-Dieu, just outside the train station.

I'll also mention that Part-Dieu long has operated well over capacity for numbers of passengers and is currently in the process of a long-term expansion affecting a major part of the city in which it is located; not just the station itself. So, be prepared for confusion, unclear signage, and short term relocation of facilities.

I just looked on RailEurope and plugged in dates in March as a straw case. Trains leave Paris from Gare Lyon and arrive at Lyon Part-Dieu. Direct, no stops, about 2 hr. On the way back to Paris, trains depart Lyon from Part-Dieu and arrive at Gare Lyon, no stops, about 2 hr.

I would use RailEurope or Trainline to book the tickets.

I would not use Trainline or Rail Europe, ticket resellers with incomplete schedules and reported refund hurdles, to buy tickets. You can download the SNCFCONNECT app and buy your tickets directly from the service provider. I use it all the time. Before it was more difficult to buy from SNCF but this new app has made it much easier.

I wouldn't buy tickets from Rail Europe either. Buy straight from the source - SNCF Connect.

What Bets and Kim said !!

I also ran CDG to Lyon and back on RailEurope, there are plenty of trains that go directly to and from CDG to Part-Dieu station in Lyon.