Hello Yume, I believe we have met at a local tourny in NC!
I have lots of experience with this matchup. I have a friend at NC State who plays Zelda as his main. I do believe you have met him at the tourny as well.
To start things, it is quite difficult to outcamp a Zelda. Her Neutral B reflects both lasers from a SHDL and if timed correctly elimates most of our approaches.
This matchup you have to play safely. Shield wisely when she is in the air in front or behind you. That is the perfect way to get a lightning kick which is either 20% damage or death at 70%. If they attempt a lightning kick on you while you shield, do an OOS Bair. The lightning kick has some major lag if it hits a shield.
Your options on the ground are bit limited in this matchup but you can work around them nonetheless. Fake your lasers to bait the Neutral B and go in with a phantasm. You can buffer CG Zelda to a fair percent. CG to spike is guaranteed kill if you get her off the edge. Try not to approach often with a dash attack. Dash attack is completely useless if the Zelda gets her Neutral B in time. A solid move to create spacing with is Ftilt. It outranges the majority of her ground attacks and pushes her away.
There are lots of moves to watch out for. Dinn's fire is easy to predict but be careful when you're on the ground. Even if you hit Zelda while in the Dinn's fire animation, most people aim the Dinn's fire down towards the stage so it goes off anyways. If you are recovering and Zelda is using Dinn's fire, a Dair or Bair will clash with the Dinn's fire causing no damage or knockback to you.
Dtilt is quite annoying for Falco. In most cases it's a tilt lock to a free attack. DI away towards the ground and shield immediately.
Her Usmash is quite strange to SDI out of. Sometimes I get out of it but I don't know how and I won't remember my button input.
Hope this helps, Yume. Ask me any more questions if you need more answers. I am probably the most experienced in the Falco vs. Zelda matchup on these boards, lol.