The string is there indeed to hang it onto a hook.
Not sure where they ended up and why they also printed smaller versions.
But some books say the smaller ones were made to fill in the small gapes of the public advertising boards, resulting in a more attractive look when close by, and also to avoid being overlapped or pasted over by newer posters.since most posters has same size , older ones were replaced (pasted over) by newer ones, the odd small ones were left alone.
In the beginning of the 1900, The Belgian state railways were the major distributor of posters, they also swapped posters with neighboring countries , mostly France.
So French posters ended up in Belgians trainstations and vice versa.
They were mostly displayed in stations, ticket sale booths, postal office , public advertising boards (or rather poles) and state buildings.
Best guess is that the smaller ones were put on cardboard and had hangers (string) to give them extra protecting and easier ease of use.
Probably they ended up in smaller postal offices or even in train wagons, but there is no real (photo) proof of this , so hard to tell...