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

No.

While the fundamental meaning of "falar" (to speak/talk) remains the same, there are significant differences in typical usage, grammar, and pronunciation:

• Typical Usage: In Brazil, "falar" is frequently used to mean "to say" (e.g., O que você falou?). In Portugal, "dizer" is the standard word for "to say," while "falar" is used specifically for the act of speaking or conversing.
• Grammar (Syntax): Brazilians frequently use proclisis, placing object pronouns before the verb (e.g., me fala). Portuguese speakers almost exclusively use enclisis, placing the pronoun after the verb (e.g., fala-me). Additionally, Brazilians use the gerund (falando) to express continuous action, whereas Portuguese speakers use the construction a + infinitive (a falar).
• Pronunciation: Brazilian Portuguese features open, clear vowels. Continental Portuguese features "vowel reduction," where unstressed vowels are often shortened or nearly silenced, making the speech sound more "closed."

Brazilian Portuguese

1. Eu quero falar com você. (I want to talk to you.)
2. Me fala o que aconteceu. (Tell me what happened.)
3. Ele está falando muito. (He is talking a lot.)
4. O que você falou para ele? (What did you say to him?)
5. Você fala muito rápido. (You speak very fast.)

Continental Portuguese

1. Eu quero falar contigo. (I want to talk to you.)
2. Diz-me o que aconteceu. (Tell me what happened.)
3. Ele está a falar muito. (He is talking a lot.)
4. O que disseste a ele? (What did you say to him?)
5. Tu falas muito depressa. (You speak very fast.)