Most of the same legal entanglements exist for trying to pitch finished projects as exist for trying to pitch "ideas." So your chances here are slim.
A game development company likely wouldn't be interested at all, simply because they are not in the business of publishing finished games... that's what a publisher is for. Unless the company is fully-independent, it's very likely they couldn't make the decision anyway, since they don't usually own the intellectual property.
A game publishing company might, since that's more in line with what they actually do. However, most of them are unlikely to entertain solicitation from unknown developers, and many of them are unlikely to be pleased with the fact that something was built using their intellectual property without permission. IP owners tend to have plans for their IP themselves, and don't need you to take it off in some random direction they don't want.
It also extremely unlikely, for the same reason, that they would consider this game "finished" even if you do: they may want their own modifications to support their future IP plans, or plans to push certain technologies they may be invested in, et cetera.
If you want to pitch an idea for a game based on a publisher's IP to a publisher successfully, you probably:
want to come at it without a "finished" product; something far along is fine, but if you present it as something that needs no additional work and thus has no opportunity for their input on their own IP you'll likely just get a cease-and-desist order.
don't actually want to incorporate their intellectual property in your pitch prototypes. Use placeholders and explain in the pitch itself that you'd like it to leverage whatever IP. This demonstrates respect for their property that you don't necessarily show when you just use it without asking and them come to them afterwards.
want to have a portfolio of games you've shipped already, or be part of a company that has developed games that sold already (and speaking officially on behalf of that company) so that somebody will actually give you the time of day in the first place.