Minitel had two huge advantages:
The hardware was free. The French PTT (Post, Telegraph and Telephone) ministry made Minitel terminals available to the public at no charge. Any French telephone user could go and collect one at a post office, and take it home and use it.
The French government provided the network, but not the content. Private service providers could use a variety of hardware - basically anything that conformed to the Minitel network standards - and deliver content of their choice to users (as long as it was legal - some services were banned for breaking the law). This was very decentralised compared to other systems.
In addition, billing was through the telephone billing system, with service providers (who could and did charge for access to their content, with 2/3 of the money going to the provider, and 1/3 going to France Telecom). This simplified payment, collecting payments, signing up for services, and provided anonymity.
These made Minitel very successful compared to other videotex services: Minitel peaked at over 9 million users, and still had over 800,000 users when the system was finally shut down in 2012. In comparison, the British Prestel system peaked at about 1% of this, with a maximum of about 90,000 users. Prestel required users to buy suitable hardware, pay for the Post Office to install a connection point, pay a monthly subscription charge for access to the network (none of which Minitel users had to pay), as well as pay for various services (which Minitel users did have to pay for).
With more users, and much more freedom for service providers, Minitel attracted many service providers. This made the system more attractive for users, which increased the number of users, which attracted more service providers, and so on. The key step was PTT making terminals available for free, which provided a sufficient user base to get this started. The content was diverse, from government services, banking, online grocery shopping, etc. through to "messageries roses" ("pink chat rooms", which PTT was not always happy about).
Minitel doesn't appear to have had any real impact on the take-up of internet access and WWW in France. Some government services were probably slower to move to the internet compared to other countries, because they were already providing the service through Minitel, but this doesn't seem to have discouraged internet users (suggesting that access to government services only motivates a small part of internet adoption).
References:
The English-language book on Minitel is:
Also of interest and freely-available online is the online version of an article they wrote in 2017 for IEEE Spectrum (July 2017 issue):