Having said that, commercial traffic isn't going to breech Irish airspace even if there is no defense, since they risk legal problems and a lack of air traffic controls.
You can check the distances by right clicking on Shannon and then selecting measure distance. You then click the SW of UK marker and then click on the marker at Paris. It works out the total distance.
Shannon to SW of UK and then over to Paris is 1,131.44 km.
Shannon to Paris direct is 905.72 km.
It is longer to have to bypass UK but not that much longer (+25%).