While you're at it, you should design your own gothic-inspired classes. In fact, you might want to rework 5e rules completely to better fit the setting. Then write your own VTT because Fantasy Grounds and d20 are, well, NIH.
...
Anyway, for once I find myself agreeing with corpsetaker. I'd love an extensively developed gothic campaign setting. I'd buy it. And, yes, I would certainly add my own elements, but I'd much rather benefit from the creative brilliance of other people, also.
I'm actually picturing a mix of gothic horror, "dark fairy tale", and a bit of La Morte d'Arthur. So lots of little kingdoms separated by especially dark and dangerous forests, scattered villages full of terrified commoners, and adversaries consisting largely of undead, fey, giants, and dragons. No BBEG responsible for this state of affair; it's just the way the world is.
If somebody kickstarts that, let me know.
What I meant, is that while you're waiting for someone else to publish such setting, it's possible to achieve a fairly good result without really having to design a lot of new stuff, but instead just cherrypick from PHB and MM what is a good match, and remove the rest.
"Gothic" has a lot to do with fear and mystery, and less to do with battle. It is also characterized by specific iconic foes which in fact D&D originally stole from "gothic literature" such as vampires, lycanthropes and golems. Here's a handful list of elements to recreate in such setting:
https://en.wikipedia.org/wiki/Gothic_fiction#Elements_of_Gothic_fiction
Probably the biggest challenge would be de-emphasizing combat. Not completely eliminate it, but at least I don't feel it should be the common way of defeating enemies and overcoming challenges, and definitely shouldn't be "flashy". I'd probably remove the vast majority of damaging spells because of that, and instead keep more subtle spells into the game. Perhaps the general presence of magic should be lowered, so you might consider removing some spellcasting classes or restrict them in level (e.g. force multiclassing), as well as avoid any magic item that is too straightforward in combat (such as a +1 weapon) and focus on items that are more situational (such as silvered weapons).
I am not sure what I would do with classes. You can keep them all or remove some... actually you can get away with just Rogue, Warlock, Fighter and Paladin. Not having a full spellcaster means magic won't solve all your problems, but you could keep the Warlock and emphasize that its magic has a price.
On the other hand, I would probably just allow human PCs. Everything else would be considered a fey or a true monster. Although this is not strictly necessary, you can definitely keep the traditional races as PCs as well.
As for monsters, for me the key would be that they should rarely operate in an open confrontation. So I would avoid the usual monstrous humanoid races such as orcs or kobolds or goblinoids or gnolls. There is a lot more "fear effect" in monsters that exist behind the curtains and mingle with humans, suggesting the possibility that humans may become those monsters as well, or that sometimes it's hard to tell them from a regular human. Vampires and lycanthropes are no-brainer of course.
You can of course add some Fear/Horror/Insanity rules system, however IMHO it's better to achieve a sense of fear in other, less straightforward ways. For example,
unbeatable monsters can be used to that purpose, with that meaning monsters that cannot be beaten in combat by hitting them with a weapon or spell, and instead you have to find another way (so ultimately they
can be beaten, just not all in the same hack&slash way). In fact IMHO "hack&slash" is pretty much the death of the fear factor; when the heroes switch from running away from zombies to chopping them down, that's when a movie ceases to be a horror and becomes a popcorn ride.
