We have purchased Eurrail first class passes for my husband and I to travel this route:
Paris-Bayeux and return (Thurs.-Fri. before Easter)
Paris - Madrid (overnight train/Easter Saturday)
Madrid-Seville -connecting on Easter morning.
Could we expect any problem boarding trains? It's been a long time since we've been on trains in Europe!!

For the Paris-Madrid and Madrid-Sevilla trains, you will have problems boarding the trains unless you have reservations: you cannot board these trains without reservations and it would be very unwise to expect to book at short notice for the Easter weekend.
Have you checked whether a pass will save money for your journeys? If these are your only train journeys, a pass will probably cost more than booking point-to-point tickets.

Actually the pass was considerably less... and has already been paid for.
Can we pay a fee to book using the pass when we get to Paris?

From Paris you have to go through Caen to get to Bayeux. Some trains are direct (reservations optional). For others you must change to a regional train in Caen (no reservations possible on that leg). They are optional for Paris-Caen.

Definitely get reservations for the Paris-Madrid night train and the Madrid-Seville train. RailEurope would be the easiest way to do this. For an additional $11 you could include either Paris-Bayeux (direct) or Paris-Caen.

When you check the supplement requirements for using the Eurail Pass on the AVE from Madrid to Sevilla, it hardly seems worth the convenience, especially when you consider the cost of booking the ticket directly with Renfe. Besides, you cannot make your reservation on-line. It has to be done at the station or through a travel agent in Spain.

http://www.interrailnet.com/1_high_speed_ave