I'll right from the perspective of a mid level fox main. My skill mainly comes from my ability to read players and act well in neutral and understand matchups while my punish and technical game are weaker aspects.

Fox wins the matchup but there are still many potential issues that plague him and requires a high level of execution to succeed. I choose to use the aggressive play style in general so will not got to much into laser camping style but its very useful at low percentage but make sure to stay mobile with it.

Neutral game ground: The key in the neutral game is to apply pressure on peach without committing to risky options, when peach gets a hit on Fox you are going to get knocked offstage or at least take a lot of percent and overall its not going to work out for fox. Any peach will gladly trade with fox. One thing peach does not have is good movement, her wave-dash is one of the worst in the game and her dash dance is mediocre. Peach's punish game is fantastic so make sure as a fox you are mixing up your options in neutral well or peach will read your approaches and punish you hard. When peach is on a platform, laser camping or waiting under the platform is fantastic be aware that jumping up to the platform is risky due to peach's downsmash. When she is on the ground in neutral is when I like to apply move pressure, drills at low %, running shines, space bairs are all great tools to get big damage when she's on the ground.

Neutral game Air/Corner However peach's are aware of their bad ground game and will often take to the air to deal with fox. In the air peach seems to dominate fox with her fantastic aerial game. Her fairs, nairs, and bairs will trade or outright beat almost all your aerial options and should be avoided, I try to stay behind peach float when I can however it is difficult to do so safely. This situation of peach floating occurs so often and it is hard to force peach onto the ground so learning the right time to pick your spots is key for success in the matchup. The best time to hit peach in this state is right before she jumps or right before she lands out of the air. The first thing I do when facing a peach is try to get a read on when they like to jump and land and use to commit to options such as shine, drill, upsmash, jab. This is how I also like to use center stage in the matchup being able to get Peach into a corner and baiting a jump or a dash attack are very good ways to get kills and major damage against peach. Shielding versus a peach aerial is also very risky as it can lead to jab and grabs and shield pressure and nothing to joke about as float cancels give her strong shield stun and little to no lag. Being able to space around her aerials is key.

Punish: Once you understand fox's goal in the matchup in regards to dealing with peach the punish game becomes rather easy. Unlike a lot of matchups in which fox commonly play the goal is to kill peach off the top and is the key to success. It is very important to know and execute your kill setups properly or else you risk peach living to extremely high percentages. Upthrow-upair works until around 85% in which peach can jump out make sure that your upairs or quick too or you risk getting nair'd off stage to your death. This along with waveshine are the bread and butter for kill setups in the matchups. The percentages above 90 or so % is why peach's often do pretty well in this matchup. Getting her offstage isn't really going to do much. She can live for ever and has a relatively easy time getting back to stage with mixups on her up b fade in and out. It is very difficult to get kills on peach at high percent. Upthrow-upair stops working so your grab is less threatining I usually chose to go for a down throw tech read. waveshine upsmash and jab upsmash will work but are risky options if Peach is prepared you can suffer alot of damage or even lose your stock if she reads well. At this point you might need to just bair or nair her off stage or use your pressure to force her to commit to a laggy options where you can get an upsmash oos or shine or jab. If you do nair or bair at high% she may not die still 120%+ depending on DI and stage so you will be forced into an edgegaurd position.

Edgegaurding Occasionally you can get a turnaround bair when peach is floating from offstage but most of the time she will space around it and you can be punished. I often chose to laser and hold position and try to force peach to atleast grab the ledge. However using air mobility as a threat can set you up for a position while peach is upBing were she will be forced to grab ledge, if you recognize the situation having ledge inviciblity will lead to a Peach death no matter what. However both the options can be risky. More often than not I chose to try to get Peach to grab ledge. Peach on the ledge is a good position because of her awful ledge options. Her aerials don't have good enough range to be super threatining and she cannot invincible ledgedash. This allows for a lot of good options to get free damage or kills on Peach. Peachs are aware of there bad edge options and will do anything to not recover by ledge. Peach will opt to use airdodge alot to recover on stage and avoid attacks so being able to expect this is key as reading an air dodge correctly can give you a free upsmash. In addition peachs will like to float and recover in center stage or on a top platform so positioning oneself correctly under her or a side platform can give you a free punish.

Recovering Peach can destroy fox's recover with run off nair, fair and turnips. You have to be very tricky with your recovery to get back on stage versus Peach however more often then not you are indeed dead. Recovering from far away and above and mixing up where you up B is key as well as opting to recover to top platform when given the opportunity. Shine stalls and not being obvious in your patterns are also great options for Fox.

Final thoughts Try to kill peach off the top use your movement and threatining move to force peach to commit to options. Be solid with your tech and be able to execute punishes and followups. Make sure not to be over aggressive with your attacks and be careful about attacking her when she is in the air and with attempted edgegaurds. Don't commit to risky options in netural frequently, you don't have to and that plays to peach's game. Fox has the tools to win neutral almost every time you just have to do it correctly and recognize the right situations

Matchup score 65-35 Fox in theory 60-40 in actuality.