Fox has a unique playstyle where combos are concerned.
To make this easier for myself to write and explain it, and hopefully for you to understand it, I'll use Falco as a comparision. Falco has shine -> dair. That basically works on a combo on anybody. He also has some great extenders for that in the form of dtilt ("the poor man's shine"), utilt, or a nair/bair. With Falco it's pretty much a flowchart for these combos. There's definitely more to this list, but I'm not very informed with Falco's combo game, so I'm definitely missing some. Basically, Falco's moves lead into each other in a way that makes him arguably the best character when used correctly.
Now Fox has a few to himself. Drill -> grab is guaranteed on Kirby/Puff, he can waveshine Peach, Falcon, Shiek, and many more across the stage and finish it off with a smash attack or grab of his choice, and he can get the "Thunder's combo" depending on an opponents actions. Also, uthrow uair. That's pretty much the Fox stuff that I know and love. The thing with Fox is that most of his moves don't set up for another move, they just cover options (note that this is from my personal experience, and this can vary from player to player, but imo this is how Fox works). But that's a great thing, because you can do anything that you want with Fox because of his amazing option coverage.
So Fox isn't very combo heavy. He's option heavy, and he is quite the force to be reckoned with when it comes to anything in Melee.