GENEVA—A shooting in southern Switzerland has left three women dead, two men wounded and raised questions about how a troubled suspect was able to go on a rampage with an old military rifle.

The shooting—which came on the eve of students’ return to classes in Newtown, Conn., after a horrific school shooting—also highlighted the easy access to firearms in gun-loving nations.

The suspect, a 33-year-old unemployed man living on disability payments, fired about 20 shots Wednesday night in the village of Daillon, authorities in the Swiss canton of Valais said Thursday.

He opened fire from his apartment and pursued people …