Why would finir be reflexive in this case? Couldn't we just say "Le cours est fini" ?
"le cours s'est fini" = "the class has finished"
"le cours est fini" = "the class is finished"
In the first sentence it's a recent past, in the second it's present.
"Le cours est fini" would be more correct. The class does not finish itself, it is not sentient...