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

Yes

The word "infelizmente" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only differences are found in pronunciation. In Brazilian Portuguese, the vowels are generally more open and the rhythm is more syllable-timed, making the word sound more melodic. In Continental Portuguese, unstressed vowels (such as the "e" in the middle of the word) are often much more closed or reduced, sometimes sounding almost silent to an untrained ear.

Brazilian Portuguese Examples

1. Infelizmente, não poderei ir à sua festa. (Unfortunately, I won't be able to go to your party.)
2. Infelizmente, o prazo para a inscrição acabou. (Unfortunately, the registration deadline has ended.)
3. Eu queria muito viajar, mas infelizmente estou sem dinheiro. (I really wanted to travel, but unfortunately I am out of money.)
4. Infelizmente, o cachorro fugiu do quintal. (Unfortunately, the dog ran away from the yard.)
5. Infelizmente, temos que cancelar o compromisso de hoje. (Unfortunately, we have to cancel today's appointment.)

Continental Portuguese Examples

1. Infelizmente, não poderei ir à tua festa. (Unfortunately, I won't be able to go to your party.)
2. Infelizmente, o prazo de inscrição terminou. (Unfortunately, the registration deadline has ended.)
3. Eu gostava muito de viajar, mas infelizmente estou sem dinheiro. (I would have liked to travel very much, but unfortunately I am out of money.)
4. Infelizmente, o cão fugiu do quintal. (Unfortunately, the dog ran away from the yard.)
5. Infelizmente, temos de cancelar o compromisso de hoje. (Unfortunately, we have to cancel today's appointment.)