In sporting events (AmE), “final” can be a noun too. “Jordan can’t play in the final. He’s still injured.” “Finale” is used outside of sports. When there is a series of acts in a performance, it would be the last one, often conveying the idea that it is exceptional or the best. “The grand finale of the firework show lasted several minutes. I’ve never seen anything like it before.”

Final is an adjective. Finale is a noun. The final act The grand finale

May I add that final is pronounced with the stress on the first syllable, but in finale, the stress is on the second.