Rosalina main here (picking up The Falcon as a secondary). I tend to like this matchup as Rosalina. I find that most falcons are impatient and rush into a lot of attacks that wouldn't happen if they play patiently.
Be weary of jabs, Rosalina and Luma can cover just about any ground approach with jabs. They can also cover a lot of space, frame trapping you if you try and roll into her.
Your main objective is getting rid of Luma. Easier said then done, but Falcon can do it fairly easily. In most cases you'll get punished for attacking Luma, but if you can separate them, take Luma out with a quick dash attack or Falcon kick, or even a gentleman. Once gone, you can do your best to combo Rosalina, but most Rosalinas will stall. Also, it doesn't help that Luma got a health buff in the latest patch.
I know Falcon benefits from platforms, but I believe Rosalina gets a better advantage from them. For the most part Falcon's recovery is very predictable. Which means Rosalina should be going for the gimp. There is nothing scarier than a Falcon with Rage, especially for Rosalina.
This may be my inexperience talking, but as Falcon, I don't try and gimp Rosalina. The risk usually isn't worth the reward when the tables can easily be turned. She can be killed easily enough from the stage with a good read.
Overall, this match up is even, maybe slightly in Rosalinas favor if she knows how to protect and keep Luma around.