If you can't take the train with your children, there is an answer - Jeune Voyageur Service (JVS).

The Jeune Voyageur Service (JVS) or Young Traveller Service, keeps your 4 to 14 year-olds amused with stories, nursery rhymes, games and songs, so that they won’t have time to get bored. JVS employees are specially trained in escorting and supervising young people. Each person is responsible for a group of a maximum of 10 children throughout the journey.
All you have to do is bring your junior globetrotter to the station 1 hour before the train departs, along with their ticket, JVS pass and completed and signed Unaccompanied Minor form and if he/she is going to Geneva, photo ID is required. Their luggage must not exceed 7kg, but don’t forget to pack a snack to keep hunger at bay! 15 minutes before arrival, the person you designate as meeting your child when making the reservation must be at the meeting point. They show proof of identity, sign the Unaccompanied Minor form and take charge of your great adventurer.

Available during major and minor school holidays, JVS is provided from and to over 130 French stations.
So don’t hesitate - entrust your young traveller to JVS!