This news report published in the newspaper Le Soir in 1939 explains how they were used;
« D'un coup de coude énergique, M. Moreau, balayeur municipal, fit sauter la glace de l'avertisseur de police ; Allo, Police-Secours ?... Un cadavre dans un sac ! Ici devant le 88, boulevard de La Chapelle ! » (With a vigourous swing of his elbow, Mr Moreau, a city street cleaner, broke the glass on the police call box: ‘Hello Police? A body in a bag ! Here in front of 88 Boulevard de La Chapelle’)
Looking at the object, situated here on the Carrefour Bineau, just at the entrance to Neuilly sur Seine, it would seem that you broke the glass (long since gone here of course), pressed the button and communicated via the grills beneath and on the ides.
Why this particular avertisseur is still standing here is not clear, but strangley enough it is situated opposite another relic from the past - an Octroi tax building I previously mentioned on this blog. My guess therefore would be that it was left behind when city limits shifted, and that nobody since has wanted to take responsibility for its removal.
Now it remains as a picturesque reminder of a non-connected past which those under 25 will probably struggle to even imagine!