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.

There are no profits. The Louvre is owned by the French government and heavily subsidized by the French taxpayer.

https://en.wikipedia.org/wiki/Louvre#Management,_administrat...

> 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]

COVID bailout:

https://news.artnet.com/art-world/france-museums-rescue-pack...

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.