Okay, I'm not that well versed in the art of Falco, but I'll share what I know about Palutena and hope it helps. I'll be discussing this with reference to her default moveset, since that's the set I'm most comfortable with.
In a nutshell, Palutena's a mixed bag overall. Her movement speed is phenomenal, her smashes are incredibly potent, her anti-air game is tremendous and her jab is a sublime setup tool - but she's also light, has immense lag on most of our moves, has to setup before getting the kill and has a very hit 'n' miss selection of specials. So we want to play up to Palutena's strengths whilst mitigating her weaknesses.
Palutena will, by her very definition, try to space you and set you up for a powerful hit. She can't just rush in and expect to win by default: she has to bide her time, watch your moves and react cautiously. Palutena thrives on mindgames and keeping you at arm's length, and since her moves are powerful but slow, she'll more often than not play carefully and defensively. You'll want to respect her space and keep an eye out for her moves; they all have pretty obvious startup animations and can be easily shielded or spotdodged if your're careful. Palutena's immensely slow hits are her constant bugbear, and something she needs to work hard to make the best of.
Palutena's got a few combos that she can use, probably the most notorious being the "divine hoo-hah": jab -> grab -> d-throw -> u-air. This can juggle for days and kills at high percents. Even if you don't DI out of it, you can airdodge it for the most part - take heed, though, as a good Palutena will watch out for this and wait until you're out of airdodge animation to u-air. Even if she doesn't throw first, it's a powerful anti-air and can catch you from below as you come down. If she can't hit with u-air, her n-air is a useful spacing tool (though it has to hit with the last frame to be of any real use), as is her f-air, and her b-air is a KO move with absolute priority and invincibility frames. D-air is pretty much useless, you'll seldom ever see it. Just try not to get caught in the air, she will catch you out and she will punish you for it.
Punishment is Palutena's bread 'n' butter. Basically any time she sees an opening, she'll exploit it or use it to her advantage. We in particular love excessive shielding (free grab!), attacks that are unsafe on shield (shieldgrab!), poor spacing (jab that!) and projectiles (if it's default set - yay reflect!). Your lasers aren't much use her, as we can just reflect them back or shield them as they come to us. Likewise, any move that we can shieldgrab, we will. Pretty much any time a grab is the optimal approach, we'll go for it. If you're within grabbing range, be wary. Our jab puts you in stunlock and allows for a grab (at low-mid percents) or, depending on DI, a u-smash (at high percents). Her jab is arguably her most powerful tool, based on potential follow-ups, and it is quite deadly if used correctly. We will almost always use single-jab rather than multi-jab, as it's the stunlock setup that's so good about it. Respect her space and don't let her get into yours.
Palutena has a number of KO options beside u-air, of course: her smashes are especially potent, but they require either huge setup or very careful timing. Hitting with an empty smash is a terrible idea for Palutena, as the endlag means she's wide open for any kind of punishment you choose. So we'll read your moves and, if we notice patterns or predictable tactics, will punish accordingly - u-smash in particular is a deadly KO tool, and it's strongest at the base. There have been many times when I've punished an unwary Falco's aerial side-b with a well-timed u-smash. She's also got a powerful dash attack that has short range and a lot of endlag, but which can KO at high percents and, like her b-air, has absolute priority and invincibility frames. You'll need to be conscious of your own moves and be wary of doing anything that can lead to her swooping in for the kill. She'll play to her strengths and make sure she's got optimal spacing to catch you and kill you.
Somebody mentioned Palutena has good tilts. Except for her d-tilt, they're all awful - slow and too much lag for what they do. Her d-tilt is a decent spacing tool, but more often than not, you'll see her jab instead. D-tilt is useful as a mix-up but not much else. Her smashes and aerials are vastly superior overall.
In short: space, pace, grab and kill. Falco is slower than a lot of characters, and this allows Palutena some breathing room - she can pace herself and space you if you're not in her face, and she'll do her best to keep you at arm's length with her spacing tools before getting her niche in for the kill. I think this matchup is in Palutena's favour, but not by a huge amount. I'm inclined to agree, based on my rather limited experience, that this is very slightly a good matchup for Palutena.
60 : 40
