The Louvre charges 17€ per person, and I'm pretty sure they're focused on fine art. How much they're profit focused versus just reinvesting profits is up for debate.
> The Louvre is owned by the French government. Since the 1990s, its management and governnace have been made more independent.[91][92][93][94] Since 2003, the museum has been required to generate funds for projects.[93] By 2006, government funds had dipped from 75 percent of the total budget to 62 percent. Every year, the Louvre now raises as much as it gets from the state, about €122 million. The government pays for operating costs (salaries, safety, and maintenance), while the rest – new wings, refurbishments, acquisitions – is up to the museum to finance.[95] A further €3 million to €5 million a year is raised by the Louvre from exhibitions that it curates for other museums, while the host museum keeps the ticket money.[95] As the Louvre became a point of interest in the book The Da Vinci Code and the 2006 film based on the book, the museum earned $2.5 million by allowing filming in its galleries.[96][97] In 2008, the French government provided $180 million of the Louvre's yearly $350 million budget; the remainder came from private contributions and ticket sales.[92]
There are also for profit museums. Not sure how profitable they actually are, but I have come across them. You'll see a lot of them around New Mexico and Arizona where you can see native american artifacts, art, fossils, etc.
