Mail won't let me quit the program and there is no force quit option

You could re-start into Safe mode, to see if that'd help fix the underlying cause; then restart normally to test.

• Use safe mode to isolate issues with your Mac - Apple Support

There are other things to do specific for Apple mail, but I don't use that with any of my Apple products.

Good luck & happy computing! 🙂

On what Apple product, with what operating system?

See if you can open Activity Monitor, then highlight Mail, then click on the force quit tiny x