Train from Lyon to Annecy. No reservation required but won't the train be full then?

Three of us are travelling from Paris to Annecy on July 11. We have made a reservation from Gare Lyons Paris to Lyons Part Dieu, and then we have to change trains in Lyons. The schedule says “No reservations required”/ “You’re ready to board”.  We are concerned that the train might be full. We also only have 12 minutes to change trains in Lyons. The train we hope to catch from Lyons to Annecy leaves at 14:08.

1. Is the afternoon train from Lyons to Annecy typically busy? Can we book a reservation, even if it says “no reservation required”? 
2. Is 12 minutes enough time for us to get from one train to another in Lyons? There is another train from Lyons to Annecy at 14:50  but we would have to change trains in Chambery, with only.a five minute stop.