Jigglypuff:
There a few things Fox needs to abuse in this matchup - Jiggly can't shieldgrab aerials if she's in the air, Fox's ground game is much better than Jiggly's, and Fox KOs vertically like a beast.
Dair is quite useful. Why? If Jigglypuff is floating toward you, she can't exactly shield grab you. This isn't just about Dair, though. You can abuse many formerly unsafe defenses/approaches as long as Jiggly is floating and flying. Don't abuse them, since air dodging is always a threat, but don't be afraid of them either. Do not, however, get hit by Bair, since you'll get juggled by it for a quick 30-50% (more if your DI sucks).
Also, your ground game beats out Jiggly's hands down. You can outspace, outrange (mostly) and simply outplay her on the ground, and the only real threat is running into her massive grab range. We've already covered Rest above - if you see it coming, use Shine to abuse those invincibility frames.
In the air, abuse Fair and Dair, but try to keep them coming from diagonals - it makes it more difficult for Jiggly to respond. Her air speed will throw you for a loop, though, so if you can avoid it, don't go to the air. Nair isn't as useful, since Jiggly will often outprioritize it, and Bair is probably best used for the kill.
Lasers: Still use them; don't expect them to be too useful, but when Jiggly dies at somewhere around 87% from Usmash, a percent or two can't hurt.
Jiggly bans Corneria, Fox bans Lylat (At least, I would.)
Fox should CP Halberd, Luigi's, maybe Rainbow Cruise (personal preference).
60:40 Fox. (Pretty close to 55:45, though.)