Interestingly, even though the oldest trees were big and tall, they did not bear flowers or fruit.
Be careful with your use of "while". It's easy to get "while" and "whilst" confused, so here I have changed yours to "Even though".
"Tall and big" sounds unnatural but, strangely, we say "big and tall" quite frequently.
We also generally refer to "fruit" as the plural of "fruit". (It's a little more complicated than that but for the purposes of this sentence, that should suffice.)