The minitel system is plain obsolete. It's text-mode, slow, and expensive. From a purely technical viewpoint, comparing it to the Internet would be comparing a Ford Model T with a Ferrari 550 Maranello.

So how is it possible that the Minitel is still alive and well, coexisting quite finely with the ever-growing Internet base ?

The answer is simple: "business model". So far, few internet companies have been able to develop a sustainable business model (ie something more profitable than "putting banner ads everywhere"). The Minitel system, on the other hand, is based on a pay-per-minute scheme. If you want to provide some service on Minitel (say, an access to some big legal database), you simply choose a pricing category (from the cheap 3614 to the $1/min 3617). When people connect to your service, they have to get through France Telecom's lines; France Telecom charge them the price you chose, keeps a part of it and gives you the rest. Ridiculous charges, maximal profit. A service provider's dream.

This is why many non-public national databases (such as Euridile, the national register of commerce) can only be accessed through the Minitel system. And this is also the reason why such a deprecated system as the minitel might well survive for years, coexisting with the cheaper, faster, better Internet system.