How much in advance do we need to purchase train tickets to travel from Paris to Bayeux?
When are you going? Buy those in advance to insure that you get the lower price tickets the sooner the better but not too far in advance that they are not on sale yet.
Most of the trains on that route are IC or IC / TER combinations. I'm not sure you'll save much with advance purchase tickets for the IC class of train. Hopefully Laura from RS will spot this thread as she will be able to provide lots of good information.
There are about six large stations in Paris, and for that trip you'll be travelling from Gare St. Lazare to Bayeux.
The Gare St Lazare to Bayeux trains are mostly Intercité trains and prices vary from 15€ to 40€ depending upon departure time and type of ticket available. Usually you can walk up and pay 15€ to 20€ for the next train. Availability is rarely a concern unless travel is on a holiday or there is some type of work action by employees.
You can easily peruse the schedules using any of these links:
You cannot purchase those tickets until 90 days prior. But sometimes, they don't list all the available options that early. In particular, there are several direct trains to Bayeux (even more to Caen), but for some reason they often don't show up online as early as other, connecting trains.