We will be attending a wedding in Lyon and then on to Paris. Babies will be 2 months and 15 months. We are concerned about managing babies and luggage on the train. Renting a car seems very expensive. 4 adults.
Man at Seat 61 says that most Paris trains start in Lyon at Perrache station.
Paris will almost certainly also be a terminus.
This should give you time to manhandle bags and babies at both ends.
https://www.seat61.com/international-trains/other-cities/trains-from-Lyon.htm
The train takes 2 hours, five hours minimum to drive,
Keep in mind if renting a car, you will need to 2 car seats, also. So larger vehicle required.
For train, SNCF Luggage Delivery Service, may be an option. I have no experience with it.
How much/size bags and paraphernalia do you expect to have? Are the adults all able to assist with bags?
Just remember that the fast trains cover the distance between Paris and Lyon much faster than a car can.
Train for sure! Far fewer hassles than by car, no need for car seats, no one-way rental fee to pay, room to move around if babies get fussy.
Train.
Put the babies in snuggly carriers so all hands are free while boarding the train.