Is there a TGV train that goes from Paris to Rouen and if so, how far in advance can we get them?
No. It is virtually a commuter line. You can buy tickets spur of the moment.
Some trains to Rouen have seat assignments and classes of seats and some price categories of tickets could sell out on those trains. For those trains, you may want to consider buying your tickets ahead of time. Other trains to Rouen are TER trains and there are no assigned seats though some of them do have first and second class seats. You can see fares and schedules at https://www.sncf-connect.com/.
Thank you for the info