Well Orange provide your web mail as part of their service which you pay for, Microsoft provide Live Mail as part of Windows that you pay for, and Google provide GMail and they make their money from advertising.
But nowadays it is not just about providing email but also digital download of music, games, films, TV shows etc (which you have to pay for), and the company you email with are more likely to be the company you also use for digital download.
So for example if you have an Android smartphone (and Android is written by Google) you normally logon to your phone with a Gmail address (also from Google) and then download apps and other media from the Google Play Store (some of which you pay for).
Same with Apple, you have an iPhone and you logon with an Apple email address then use Apple iTunes.
And of course all these companies (Amazon, Microsoft, Google, Apple, etc) want you to logon to your devices with THEIR email address so you use THEIR digital download (that is where the money is).
That is why you now need to logon to Windows 10 with a Microsoft email address, and that is why Amazon now sell their "Fire" tablets (so you can download media from the Amazon store).
So it is not so much about offering email for free, but about having as many people using your computer systems so they have a "captive" audience who will then download digital media.
Remember much music is now downloaded from iTunes or Amazon and not bought on physical CDs. Same goes for films and games and TV shows.
It is the future.