The “B” in BBOX stands for “Bouygues”, which is one of the four major suppliers of internet connection in France.
The other three are Orange, Free … and SFR.
There are a plethora of offerings but not that many actual network-owners - that is, the companies that actually set up the network. The above mentioned four carriers broker their connections to a good number of others who resell the service. My bank actually does this!
According to latest reports Orange has the largest 4G-coverage in France. But, in general, France is a laggard regarding 4G, one of the most important Internet communication systems today. (The other three being fiber-optic, DSL and Satellite.)
Availability of offerings is obvious dependent upon where you live. If you reside in a large city, you have a good choice offerings. If you live in the countryside, go for a satellite connection because 4G is laggard in terms of antennas installed.
Try as I may, I cannot find one antenna-company willing to install a 4G antenna (which is really quite tiny) on my TV mast. And the DSL in the countryside is ridiculously slow.
I was curious so I kept my DSL-connection whilst putting in a 4G receiver box. I measured bandwidth download times in both instances; that is, via DSL and 4G.
The 4G connection was between 2 and 3 times quicker. (BUT, if you live in a rainy part of France, be careful because the weather will indeed affect signal-strength! Which does not happen on a DSL line via the telephone network. But DSL is very, very slow in the countryside because too many people are connected and the service is not being upgraded technologically.
Do not choose the “VDSL” option (supposedly better than “ADSL”), which I had and was painfully slow. VDSL degrades seriously if a connection is beyond 1.6kms from the local central-box.