Flight from Ireland to Normandy

If you want to avoid Paris the best you will be able to do is Dublin to Nantes (which is in neighboring Brittany) on Ryanair.
Then just take the train bus or rent a car.

Could you fly to London, then take the Chunnel over to Paris, then train to Normandy?
As far as I know, flying INTO Paris isn't necessarily a problem -- it's flying OUT of Paris that is difficult. :)

Farther out than Nantes is Bordeaux, but Bordeaux would probably give you more choice of flights.

You can get to Rennes on a one-connection itinerary, but given that rail lines in France fan out from Paris, I suspect you'll do better by flying into that city and hopping on a train. Most other potential arrival points will probably require you to take the train into Paris and head back out again (been there, done that--3 times this summer).

Irish Ferries runs a ferry between Dublin and Cherbourg. The (overnight) trip takes about 19-20 hours. Makes flying into Paris sound like a good option, doesn't it?