Giroud netted the opener to join Zinedine Zidane as France's fourth highest all-time leading goalscorer and Nabil Fekir claimed the second before the break as Les Bleus kept their first clean sheet in four games.
They also have scored two goals or more in their last six matches.
France will take on Australia, Denmark and Peru in World Cup Group C. Ireland have not qualified for the finals.
France coach Didier Deschamps left his best striker Antoine Griezmann on the bench with Fekir starting alongside Giroud and Kylian Mbappe and the decision paid off.
Giroud scored his 31st goal in 72 internationals in the 40th minute. His header from Fekir's corner was saved on the line by Colin Doyle but the Chelsea striker poked in the rebound.
Only Thierry Henry (51), Michel Platini (41) and David Trezeguet (34) have scored more goals for France.
Three minutes later, Doyle's error helped Fekir double the tally with a powerful shot from just inside the box.
Ireland failed to muster a single attempt on target until stoppage time, when France keeper Steve Mandanda denied Shaun Williams.
(Reporting by Julien Pretot; Editing by Ed Osmond)
