The service was provided for free to the government, the company organised free training sessions for government clerks, and it was the driving schools who paid for the service when dialling into our minitel servers.
It technically wasn't a monopoly, because the driving schools could still go down to the préfecture, and do everything using the forms/pen/paper.
The company tried on a number of occasions to get the driving schools to move from the Minitel service to the new web version. Every single time, there was a huge push-back from the driving school unions, about how expensive the new service was, and how "unusable" the website was, compared to the Minitel.
We even had people calling in, saying that we were extortionists. "We've been using this for over 20 years, and never paid a cent; now you want us to pay xx€ a month?" I guess some of them really didn't look at their phone bill.
I heard about 4 or 5 "planned terminations" of the Minitel service during my stint from 2010 to 2015. France Telecom/Orange even provides a "Minitel over IP" service these days, where a website can be enrolled into their payment service, and users pay per minute on the website. It's a superb scam tool (just have a hidden iframe open a pay-as-you-go page), and Orange is constantly fighting the fraudsters.