I’ve seen this alternately translated as “livraison des bagages,” “réclamation de bagages,” and “arrivée des bagages.” Which is the most common?
My impression is the signs only say bagages in airports but if you need something specific, you might use any of these :
[zone de] récupération des bagages.
[zone de] retrait des bagages.
[zone de] livraison des bagages.
Réclamation would be the desk where you complain about missing or damaged luggage and arrivée, when referring to an area, is more likely to be related to passengers while arrivée des bagages would rather tell the time of their arrival.