Another vote for the plane. Unless you have a hatred of flying, a desire to see a lot of trains, and would consider stopping off en-route.

Depending on your Ireland itinerary, you don't necessarily need to pass through the UK. Brittany Ferries has an overnight ferry from Cork to Roscoff (Brittany, France). From there, you can take a day train to Paris - arriving around lunchtime. From Paris, it's at least 8 hours with at least 1 change. Same-day connection just about doable, but better to stop off in Paris.

In short, take the plane.