PARIS—Next year, Minitel—France's precursor to the Internet—will finally meet its maker.

For 30 years the toaster-sized screen weathered the Internet revolution. Despite a text-only service, basic graphics and snail-like speed, the terminal generated €30 million ($43.1 million) in revenue in 2010, with around 85% redistributed to service providers such as banks and weather forecasters, according to France Télécom SA, which operates the service.

Despite...