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

Yes

The word "fruta" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated, and the rhythm is more syllable-timed. In Continental Portuguese, the unstressed vowels (such as the "u" in "fruta") are often more closed or even reduced, and the rhythm is more stress-timed.

Brazilian Portuguese

1. Eu adoro comer fruta no café da manhã. (I love eating fruit for breakfast.)
2. Essa fruta está bem docinha. (That fruit is very sweet.)
3. Vamos comprar fruta na feira hoje? (Are we going to buy fruit at the street market today?)
4. Tem muita fruta na geladeira. (There is a lot of fruit in the refrigerator.)
5. Você prefere fruta ou doce? (Do you prefer fruit or sweets?)

Continental Portuguese

1. Eu adoro comer fruta ao pequeno-almoço. (I love eating fruit for breakfast.)
2. Esta fruta está muito doce. (This fruit is very sweet.)
3. Vamos comprar fruta ao mercado hoje? (Are we going to buy fruit at the market today?)
4. Há muita fruta no frigorífico. (There is much fruit in the fridge.)
5. Preferes fruta ou doces? (Do you prefer fruit or sweets?)