I finally talked to American Airlines and they helped me book flights with one of their partners (Iberia Airlines). The tricky part about this change was that we would need to get to a different airport in Paris. What did we ever do without the internet? It was fairly easy to figure out the various options (bus, taxi, train). Someone had even posted several pictures of the Paris airport showing how to navigate from the airline terminals to the train terminal and to the bus locations. Bus looked easy as there was a direct route from one airport to the other.
Our new plans were completed the day we got the EasyJet email. The following day, I get another email from EasyJet saying
"Dear Customer: If you received an email earlier tonight that your flight was cancelled, please ignore the previous email. Your flight is NOT cancelled. We would like to sincerely apologize for the inconvenience caused by this technical error. We are writing to let you know that we have had to reschedule some of our flights. Unfortunately, your flight is one of those affected."
The message went on to say the flight times had changed so instead of a 1:30pm departure, the flight would depart at 5:30pm.
At this point we have flights booked with two different airlines - Iberia and EasyJet. Luck was on our side because shortly after getting the second EasyJet email, I get a call from American saying the Iberia flights couldn't be confirmed because the carrier wasn't actually Iberia - it was with another airline and since they weren't a partner with American, the tickets couldn't be purchased through American. Problem solved. (almost solved - I won't go into details about American having mailed paper tickets and the process I had to go through to get a refund - even though those paper tickets apparently werent' any good).
Next trip - I may have to defer to the travel agents to arrange the flights!