Fresh cilantro is パクチー. It used to be rare in Japan, but most supermarkets now have small packs in the herb section.
パクチー
pakuchī
香菜
shanzai / kōsai
コリアンダー
koriandā · usually the seeds or powder
In the shop
Produce, in the herb corner with basil and mint, or next to the lettuce.
Which shops
Most large supermarkets. Cheaper in bigger bunches at Asian grocery shops.
Watch out
コリアンダー on the spice shelf is ground coriander seed, not the leaves.
Lazy Recipe sees that you're in Japan and turns any dish into 3 steps with what Japanese supermarkets sell. Your shopping list shows each item's Japanese label and aisle.