Is the word perfume the same in Brazilian and European Portuguese?

Yes

The spelling and meaning of "perfume" are identical in both Brazilian and Continental Portuguese. The only difference lies in the pronunciation (phonology):

• Brazilian Portuguese: The unstressed vowels are more "open" and clearly articulated. The first "e" is typically pronounced as an open [e], and the final "e" is pronounced clearly as [i].
• Continental Portuguese: Unstressed vowels undergo significant reduction. The first "e" is a closed, nearly silent [ɨ] (similar to a muffled sound), and the final "e" is also heavily reduced or "swallowed."

Brazilian Portuguese Examples

1. Eu gosto muito desse perfume. (I like this perfume a lot.)
2. Esse perfume tem um cheiro doce. (This perfume has a sweet scent.)
3. Você comprou um perfume novo? (Did you buy a new perfume?)
4. O perfume dele é bem forte. (His perfume is quite strong.)
5. Eu quero um perfume que dure bastante. (I want a perfume that lasts a long time.)

Continental Portuguese Examples

1. Eu gosto muito deste perfume. (I like this perfume a lot.)
2. Este perfume tem cheiro a baunilha. (This perfume smells like vanilla.)
3. Compraste um perfume novo? (Did you buy a new perfume?)
4. O perfume dele é muito forte. (His perfume is very strong.)
5. Quero um perfume que dure imenso. (I want a perfume that lasts a lot.)