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

No

While the spelling and core concept of "feira" remain the same, there are differences in typical usage and nuance between the two dialects:

1. Primary Association: In Brazil, "feira" is the standard, ubiquitous term for the weekly, open-air street market where people buy fresh produce. In Portugal, while "feira" is used for these markets, the term is more frequently associated with organized, periodic events (e.g., feira de artesanato or feira de automóveis), whereas the regular food market is often referred to as "mercado".
2. Weekdays: In Brazil, the expression "dia de feira" is a common, slightly informal way to refer to a weekday (as opposed to the weekend). In Portugal, the standard and natural way to express this is "dia de semana".

Brazilian Portuguese usage:

1. "Vou à feira comprar frutas e verduras." (I am going to the market to buy fruit and vegetables.)
2. "A feira de hoje está muito cheia." (Today's market is very crowded.)
3. "Não gosto de trabalhar em dia de feira." (I don't like working on weekdays.)
4. "A feira de ciências da escola foi um sucesso." (The school science fair was a success.)
5. "Comprei tudo fresquinho na feira." (I bought everything fresh at the market.)

Continental Portuguese usage:

1. "Vou ao mercado comprar legumes." (I am going to the market to buy vegetables.)
2. "A feira de artesanato é amanhã." (The craft fair is tomorrow.)
3. "Não trabalho em dia de semana." (I don't work on weekdays.)
4. "Fui à feira do livro ontem." (I went to the book fair yesterday.)
5. "O mercado municipal está muito movimentado." (The municipal market is very busy.)