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

Yes

The only difference between the word "azul" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazilian Portuguese, the "l" at the end of the word is vocalized, meaning it is pronounced as a "u" sound (sounding like a-zu). In Continental Portuguese, the "l" is a clear, alveolar lateral consonant, where the tongue touches the roof of the mouth (sounding like a-zul).

Brazilian Portuguese

1. O céu está muito azul hoje. (The sky is very blue today.)
2. Eu comprei uma camisa azul. (I bought a blue shirt.)
3. Ela gosta de usar vestido azul. (She likes to wear a blue dress.)
4. Eu estou amando esse azul do mar. (I am loving that blue of the sea.)
5. A caneta azul sumiu. (The blue pen disappeared.)

Portuguese (Continental)

1. O céu está muito azul hoje. (The sky is very blue today.)
2. Comprei uma camisa azul. (I bought a blue shirt.)
3. Ela gosta de usar um vestido azul. (She likes to wear a blue dress.)
4. Estou a adorar esse azul do mar. (I am loving that blue of the sea.)
5. A caneta azul perdeu-se. (The blue pen was lost.)