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

No

While the spelling and the fundamental concept of the verb (to speak/talk) are the same, there are differences in typical usage and pronunciation:

• Usage: In Brazilian Portuguese, "falam" is frequently used as a synonym for "dizem" (they say/they tell) when conveying information. In Continental Portuguese, "falam" is almost strictly reserved for the act of speaking or talking, whereas "dizem" is the standard word for conveying information or "saying" something.
• Pronunciation: In Brazilian Portuguese, unstressed vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction, meaning the "a" in "falam" is much more closed, compressed, or even nearly swallowed.

Brazilian Portuguese Examples

1. Eles falam que vai chover. (They say it is going to rain.)
2. O que eles falam de você? (What are they saying about you?)
3. Eles falam que o restaurante é bom. (They say the restaurant is good.)
4. As pessoas falam que ele é legal. (People say he is cool.)
5. Eles falam que o trabalho acabou. (They say the work is finished.)

Portuguese Examples

1. Eles dizem que vai chover. (They say it is going to rain.)
2. O que é que eles dizem de ti? (What are they saying about you?)
3. Eles dizem que o restaurante é bom. (They say the restaurant is good.)
4. As pessoas dizem que ele é simpático. (People say he is nice.)
5. Eles dizem que o trabalho acabou. (They say the work is finished.)