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

Yes

The word "fizeram" is identical in both Brazilian and European Portuguese regarding its spelling, grammatical function (it is the third-person plural of the verb fazer in the pretérito perfeito do indicativo), and meaning. The only differences are phonetic, specifically in the way unstressed vowels are articulated and the subtle variations in the intensity of the nasalization in the final syllable.

Brazilian Portuguese

1. Eles fizeram o bolo de chocolate. (They made the chocolate cake.)
2. As crianças fizeram muita bagunça. (The children made a lot of mess.)
3. Eles fizeram o dever de casa. (They did their homework.)
4. Eles fizeram um lanche com suco. (They made a snack with juice.)
5. Eles fizeram o registro no ônibus. (They made the registration on the bus.)

European Portuguese

1. Eles fizeram o bolo de chocolate. (They made the chocolate cake.)
2. As crianças fizeram muita confusão. (The children made a lot of mess.)
3. Eles fizeram os trabalhos de casa. (They did their homework.)
4. Eles fizeram um lanche com sumo. (They made a snack with juice.)
5. Eles fizeram o registo no autocarro. (They made the registration on the bus.)