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

Yes

The word "sempre" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction; the "e" in "sempre" is often shortened or nearly silent, resulting in a more closed, clipped sound.

Brazilian Portuguese Examples

1. Eu sempre vou te amar. (I will always love you.)
2. Ela está sempre sorrindo. (She is always smiling.)
3. Nós sempre chegamos atrasados. (We always arrive late.)
4. Você sempre esquece suas chaves. (You always forget your keys.)
5. Sempre tem comida na geladeira. (There is always food in the fridge.)

Continental Portuguese Examples

1. Eu sempre te amarei. (I will always love you.)
2. Ela está sempre a sorrir. (She is always smiling.)
3. Nós sempre chegamos atrasados. (We always arrive late.)
4. Tu esqueces sempre as tuas chaves. (You always forget your keys.)
5. Há sempre comida no frigorífico. (There is always food in the fridge.)