I've played few friendlies with Prof before, so I can feel your pain lolol :D
I think we can assume that you're not losing just because you're not playing your character/the MU correctly, but you're just being constantly outplayed by a player that is much better than you. This means that he's faster, more technical and more precise than you. He can easily pick up on your habits and exploit your approaches/defensive tactics, if you're being predictable. I guess he also has a lot more experience than you, so it's easier for him to act and react quickly, while you're being hindered by your inexperience and imperfect tech skills.
This means that even if your neutral game was as good as Prof's, the matches wouldn't be close because when he gets a hit, he can properly follow up and do A LOT of damage, while you're forced to play a "hit and run" game, meaning that you'll need to outplay him at least 3-4 times before you can take a stock.
Except for practicing tech skill and improving both your neutral and punishment game, I'd advise you to carefully watch top level Falcos play against Fox players. This means studying Mango/PeePee/Westballz/Shiz/Chops/Zhu vids and trying to understand why they're doing something at a given moment. This will help you improve your combo game AND understand how to condition your opponents better.
E.g.: "I'm trying to space around my opponent's shield, but if I hesitate before going in he'll retreat safely to a platform. What could I do to counter this?" - If you carefully watch other Falco's play, you'll notice there are various answers to this. An example would be Mango's typical full hop Nair approach on platforms, which is great to counter platform-happy Foxes. If you don't feel confident jumping at them like that, you can study how PP/Zhu are keeping the center of the stage and capitalizing on they're opponents' movement when they come down from the platform. Or watch how Shiz/Chops deal with campy Foxes with their amazing platform-lazer game, etc.
Just remember that you're not playing against a TAS Fox. As good as your opponent might be, he's still an human being, and as such he has exploitable patterns/weaknesses that you should be punishing as harder as you can.
Hope this helps :D