There are free lessons for migrants in 'precarious situations', either social or economic (http://www.francaisenjeu.ch/
). I know of expats who were able to access these lessons.
There is also the association Lire et Ecrire (http://www.lire-et-ecrire.ch/page.php
) which is primarily aimed at combating illiteracy, but which, if I have correctly understood, is also open to non-native speakers of limited means (I used to have a physiotherapist who volunteered there).
And some non-native speakers who receive social aid or unemployment benefits may be offered language courses.
But as far as I know, there are no free lessons automatically offered to people who move here.